UNIVERSITY   OF  CALIFORNIA 

•ARCHITECTURAL   DEPARTMENT   LIBRARY 


GIFT  OF 
Mrs*   George  Beach 


AN 


ELEMENTARY    COURSE 


CIVIL  ENGINEERING 


FOB   THE   DSJt  OJ" 


CADETS  OF  THE  UNITED  STATES  MILITARY  ACADEMY. 


BY 


J.    B.   WHEELEK, 


of  Civil  and  Military  Engineering  in  tAe  United  State*  Military  Acadcm* 
Wett  Point,  N.  r.,  and  Brevet-Colonel  U.  S.  Army. 


FIFTH    EDITION. 


THIRD   THOUSAND. 


NEW   YORK: 

JOHN   WILEY  AND   SONS, 
53  EAST  TENTH  STKEET, 


A 


CkjPYRIOHTKD,    1878,    B» 

JOHN  WILEY  &  SONS 


Press  of  J.  J.  Little  &  Co, 
Astor  Place,  New  York. 


PREFACE. 


THIS  text-book  is  prepared  especially  for  the  cadets  of  the 
United  States  Military  Academy,  to.  be,  used  while  pursuing^ 
their  studies  in  the  course  of  Civil  Engineering  laid  down  for 
them. 

The  object  of  the  book  is  to  state  concisely  ffie  principles  of 
the  science  of  Civil  Engineering,  and  to  illustrate  these  prin- 
ciples by  examples  taken  from  the  practi.de  and  writings  of 
civil  engineers  of  standing  in  their  profession. 

These  principles  and  facts  are  widely  known  and  are  famil- 
iar to  all  well-informed  engineers ;  they  will,  however,  be  new 
to  the  beginner. 

The  present  edition  differs  slightly  from  the  one  that  has 
been  used  for  the  past  seven  years.  The  modifications  in  the 
text  are  simply  those  that  have  been  suggested  by  the  use  of 
the  book  in  the  class-room.  The  differences  between  the  two 
editions  are,  however,  not  sufficiently  great  to  prevent  a  simul- 
taneous use  of  both  old  and  new  in  the  same  class. 

J.  B.  W. 

WEST  POINT,  N.  Y.,  July,  1884. 


812397 


CIVIL  ENGINEERING. 


CONTENTS. 


INTRODUCTION ». xvii 

PART  L 

Building  Materials. 
CHAPTER   L— WOOD. 

4BTICLE  PAGH 

2.  Timber,  kinds  of 1 

3.  Timber  trees,  structure  of 2 

4.  Timber  trees  classed 2 

5-9.     Soft-wood  trees,  examples  of 3 

10-12.  Hard-wood  trees,  examples  of 4 

13.  Age  and  season  for  felling  timber 5 

14.  Measurement  of  timber. 6 

15.  Appearances  of  good  timber 6 

16.  Defects  in  timber 7 

17.  Seasoning  of  timber — natural  and  artificial 7 

18.  Durability  and  decay  of  timber — wet  and  dry  rot 8 

19-24.  Durability  under  certain  conditions  and  means  of  increasing  it.  9 

25.  Preservation  of  timber  in  damp  places 10 

CHAPTER  II.— STONE. 

26.  Qualities  requisite  in  stone  for  building 13 

27.  Stones  classed — natural  and  artificial 14 

L  NATURAL  STONESI 

28-31.  Remarks  on  the  properties  of  natural  stone— strength,  hardness, 

and  durability 14 

3&-34.  Effect  of  heat  and  cold  on  stone 15 

35.  Preservation  of  stone 17 

36.  Ease  of  working  stone 17 

37.  Quarrying 18 

Varieties  of  Building  Stones. 

38.  Silicious  stones 18 

89.        Argillaceous  stones 20 

40-42.  Calcareous  stones,  marbles,  common  limestones 21 

IL  ARTIFICIAL  STONES. 

1.  Brick. 

43.  Brick 23 

44.  Sun-dried  brick. 23 

45.  Burnt  brick 23 


CONTENTS.  VU 


46-49.    Common  brick — size  and  manufacture 24 

50.  Qualities  and  uses  of  brick 26 

51.  Characteristics  of  good  brick 26 

52.  Varieties  of  common  brick 26 

53-54.     Pressed  and  fire  bricks 27 

55.  Brick-making  as  one  of  the  arts 27 

56.  Tiles. 27 

2.  Concrete*. 

57-59.     Concrete,  its  composition,  manufacture  and  uses 28 

60-62.     Patent  stones — Beton  Agglome're,  and  Ransome's  patent  stone  29 

3.  Asphaltic  Concrete. 

63.          Asphaltic  concrete,  composition,  manufacture,  and  uses 31 

4.   Glass. 

64-65.    Glass,  composition  and  uses— glazing 33 

CHAPTER  IIL— METALS. 

66.  Metals  used  in  engineering  constructions 32 

67.  Ironandsteel 32 

68-71.     Cast  iron — varieties,  appearances  of  good  cast  iron,  test  of 

quality,  indications  of  strength 33 

72-73.     Wrought  iron — Appearance  of  good  wrought  iron— Forms- 
Iron  wire 34 

74-78.     Steel — General  modes  of  manufacture — Varieties — Hardening 

and  tempering 36 

79.  Durability  of  Iron  and  steel 38 

80.  Protection  of  iron- work. 39 

81-85.     Copper,  zinc,  tin,  lead,  alloys, 40 

CHAPTER  IV.— UNITING  MATERIALS. 

86.  Uniting  materials 41 

87.  Glue 41 

88.  Lime,  varieties  of 42 

89-91.     Limestones,  hydraulic  and  ordinary 42 

92.          Characteristics  and  tests  of  hydraulic  limestone 43 

93-97.     Calcination  of  limestones — Kilns,  intermittent  and  perpetual 

—Object  of  kilns 44 

98-104.  Products  of  calcination,  common  lime,  hydraulic  lime,  hy- 
draulic cement,  and  pozzuolanas 48 

105.          Trass 51 

106-108.  Manufacture  of  limes  and  cements 51 

109-113.  Manufacture  of  slow-setting  and  quick-setting  cements  from 

argillaceous  limestones 53 

114-115.  Hydraulic  cements  from  other  stones 54 

116.          Scott's  hydraulic  cement 55 

117-118.  Tests  for,  and  the  storage  of  limes  and  cements. 56 

119.           Mortar — common  and  hydraulic 57 

120-121.  Slaking  lime,  and  the  preservation  of  slaked  lime 58 

122.           Sand,  varieties  of,  and  uses  in  mortar 6C 

123-126.  Manufacture  of  mortar,  proportions  of  ingredients,  and  mani- 
pulation   61 

127-128.  Setting  of  mortar,  theory  of 63 


CONTENTS. 


129-132.  Adherence,  hardness,  strength,  durability,  and  uses  of  mortar.  64 

133-137.  Mastics,  bituminous  and  artificial— uses 67 

CHAPTER  V.- PRESERVATIVES. 

138-139.  Paints 69 

140-145.  Japanning,  oiling,  varnishes,  coal  tar,  asphaltum,  metal  cov- 
erings.   70 

146.          Preservatives  based  upon  chemical  combinations 71 


PART  H. 

Strength  of  Materials. 
CHAPTER  VI.— STRAINS. 

147.          General  problems 72 

148-149.  Strength  of  materials — strains— stress 72 

150-152.  Classification  of  strains 73 

153-157.  Constants — weight,  limit  of  elasticity,  coefficient  of  elasticity, 

modulus  of  rupture 77 

Tension. 

158.  Elongation  of  a  bar  by  a  force  acting  in  the  direction  of  its 

axis. 81 

159.  Tensile  strength  per  square  inch  of  certain  building  materials.  82 

160.  Work  expended  in  the  elongation  of  a  bar 83 

161.  Elongation  of  a  bar,  its  weight  considered 85 

162-163.  Bar  of  uniform  strength  to  resist  elongation 86 


164.  Modulus  of  resistance  to  crushing 

165.  Values  of  C  for  certain  building  materials. 


Shearing. 

166.  Kinds  of  shearing  strains — coefficient  of  lateral  elasticity — 

modulus  of  shearing 90 

167.  Values  of  S  for  certain  materials 92 

Transverse  Strain. 

168-169.  General  equation  expressing  the  relation  between  the  moments 
of  the  external  forces  bending  the  bar  and  the  moments  of 

the  resistances 92 

170.  Shearing  strain  produced  by  a  bending  force 98 

171.  Changes  in  form  of  the  bar 98 

172.  Stress  on  the  unit  of  area 99 

173.  ValuesofI 99 

Flexure. 

174.  General  equation  of  the  elastic  curve 100 

175.  Bar  fixed  at  one  end  and  acted  on  by  a  force  at  the  free  end 

to  bend  it 102 

176-181.  Beam  resting  on  two  points  of  support 103 

182-183.  Beam  having  its  ends  firmly  held  down 109 


CONTENTS.  IX 


184.          Beam  fixed  at  one  end  and  the  other  end  resting  on  a  support.  113 

185-186.  Beam  resting  on  three  points  of  support 114 

187-194.  Theorem  of  three  moments  and  applications 117 

Torsion. 

195.  Coefficient  of  torsional  elasticity  .                                 125 

196.  Valuesof  G 127 

197.  Rupture  by  twisting. 127 

198.  Influence  of  temperature 128 

CHAPTER  VII— STRENGTH  OF  BEAMS. 

199.  General  problems 128 

200.  Strength  of  beams  of  uniform  cross-section  strained  by  a  ten- 

sile force  129 

201.  Strength  of  beams  of  uniform  cross-section  under  compressive 

strains 129 

202.  Hodgkinson's  formulas 130 

u             Gordon's  formulas 131 

"            C.  Shaler  Smith's  formula 132 

203.  Deductions  made  by  Mr.  Hodgkinson 132 

204.  Strength  of  beam  to  resist  shearing 134 

205.  Strength  of  beam  to  resist  rupture  by  bending 134 

206.  Formulas  for  maximum  stress  on  the  unit  of  area  in  the  dan- 

gerous section. 135 

207.  Safe  values  f or  R' 136 

208.  Influence  of  form  of  cross-section  on  the  strength  of  a  beam .  137 

209.  Strongest  beam  of  rectangular  cross-section  that  can  be  cut 

from  a  cylindrical  piece 138 

210.  Beams  of  uniform  strength 139 

211-215.  Beams  of  uniform  strength  to  resist  transverse  strain 140 

216.  Relation  between  the  stress  on  unit  of  area  and  deflection 

in  a  beam  produced  by  bending  forces 144 

217.  Action  of  oblique  forces 145 

218.  Strength  of  beams  against  twisting 146 

219-220.    Strength  of  a  beam  strained  by  rolling  loads 147 

221-222.    Limits  of  practice  and  factors  of  safety 151 

223-224.    General  equation  between  the  moments  of  the  external  forces 

and  the  moments  of  the  resistances  in  curved  beams 152 

225-227.    Method  of  determining  the  equation  of  mean  fibre,  the  un- 
known reactions,  and  the  stress  on  unit  of  area 155 

228.  Approximate  method  of  determining  stresses  in  a  curved 

beam  resting  on  two  supports 160 

229.  Curved  beam  with  ends  firmly  fixed 162 


PART  m. 
CHAPTER  Vin.— FRAMING. 

230-231.  Art  of  construction — frames— carpentry 163 

232.  Joints 164 

233-239.  Joints  in  timber- work 165 

240.  Fastenings  of  joints 171 

241.  General  rules  for  construction  of  joints. 172 

242-248.  Joints  for  iron-work. 173 

249.  Simple  beams 178 


CONTENTS. 


ABTICLK 

250.  Solid-buHt  beams  ........................................  178 

251.  Framing  single  beams  with  intermediate  supports  ...........  180 

252.  Open-built  beams  —  king  and  queen  post  trusses  .............  181 

253.  Necessity  for  braces  where  rigidity  is  required  ............     183 

254-25">.  Stresses  in  an  inclined  beam  ............................     183 

256-257.  Stresses  in  a  triangular  frame  ...........................     187 

253.          Stresses  in  a  jib-crane  ........  ..........................     189 

259.          Combined  triangular  frames.  ..............................   191 

260-262.  Triangular  bracing  .......................................  191 

263.  Vertical  and  diagonal  bracing  .............................  194 

264.  Angle  of  economy  ........................................  196 


PART  IV. 

CHAPTER  IX.— MASONRY. 

265.  Definition  of  masonry « 198 

266.  Kinds  of  masonry  structures 198 

267.  General  definitions 199 

268.  Retaining  and  reservoir  walls  and  dams 199 

269.  Areas,  lintels,  and  plate-bands 200 

270-271.  Arches  and  their  classification 201 

272-279.  Cylindrical,  groined,  cloistered,  annular  arches,  domes,  etc.  201 

Mechanics  of  Masonry. 

279.          Distribution  of  pressure  on  a  surface 205 

280-286.  Normal  pressure 205 

287.  Oblique  pressure. 210 

288.  Strains  on  structures  of  first  and  second  classes 211 

289-296.   Strains  on  retaining  walls 211 

297-298.  Counterforts. 221 

299-300.   Reservoir  walls  and  dams 222 

301.  Strains  on  structures  of  fourth  class 224 

302-303.  Arches  and  modes  of  yielding 224 

304-305.  Conditions  of  stability  for  arches 225 

306.  Joints  of  rupture 227 

307-309.  Conditions  of  equilibrium  for  a  full-centered  cylindrical  arch.  228 

310.  Rankine's  rule  for  obtaining  approximate  value  of  horizontal 

thrust 231 

311.  Curves  of  pressure  and  of  resistance 233 

312-316.  Equation  of  the  curve  of  resistance 233 

317.          Depth  of  keystone 236 

318-319.  Thickness  of  piers  and  abutments,  and  table  of  dimensions 

for  arches  of  small  spans 237 

320.  Forms  of  cylindrical  arches , 237 

321.  Rampant  and  inverted  arches 238 

822.          Wooden  arches 238 

CHAPTER  X.— MASONRY  CONSTRUCTION. 

824-325.  Rubble  masonry 239 

826-327.  Ashlar  masonry 241 

828.  Cut-stone  masonry ."    . . . . .  242 

829.  Stone-cutting. 343 

830-333.  Strength  of  masonry . . .  *  243 

884-336.  Machinery  used  in  constructing  masonry  work 248 


CONTENTS.  XI 

ABTTCLK  PAGE 

337_344.  Brick  masonry  and  construction 251 

345.  Construction  of  concrete  masonry 253 

346_349.  Construction  of  retaining  and  reservoir  walls 255 

350.  Construction  of  areas,  lintels,  etc 257 

351.  Form  of  soffit  of  the  arch 258 

352-357.  Ovals 258 

358.  Construction  of  voussoirs 263 

359.  Bond  in  arches 264 

360.  Oblique  or  askew  arches ,  265 

361-363.  Construction  of  arches 266 

364-366.  Cappings,  abutments  and  piers,  and  connection 268 

367.  Machinery  used  in  constructing  arches 270 

368-369.  General  remarks  on  the  arch 272 

370.  General  rules  to  be  observed  in  constructing  masonry 273 

871-375.  Preservation  and  repairs  of  masonry 274 

876.  Mensuration  of  masonry 276 


PART  V. 
CHAPTER  XI.— FOUNDATIONS. 

377.          Definition  of  foundation 277 

379.  Yielding  of  foundations 277 

380.  Natural  and  artificial  beds  of  foundations 278 

381.  Classification  of  soils 278 

Foundations  on  Land. 

382-383.  In  rock,  compact  earth,  etc 278 

384.           In  ordinary  soils 280 

385-386.  In  soft  earths  and  compressible  soils 280 

387-393.  Piles,  and  kinds  of 282 

394-397.  Piles,  how  forced  in  the  soil 286 

398.          Load  allowed  on  piles 288 

399^01.  Bed  of  foundation  made  of  piles 288 

CHAPTER  XII.— FOUNDATIONS  IN  WATER. 

402.          Difficulties  met  with 290 

403-404.  Concrete  beds 290 

405.  Beds  of  piles 292 

406.  Common  caisson 292 

407.  Permanent  caissons 294 

408.  Submarine  armor  and  diving-bell 294 

409.  Pierre  perdue 295 

410.  Screw  piles 295 

411.  Well  foundations 295 

412.  Iron  tubular  foundations. 296 

413-414.  Exclusion  of  water  by  earthen  dam 297 

415-418.  Cofferdam 297 

419-420.  Caisson  and  crib-work  dams 300 

422-424.  Pneumatic  pile 302 

425.           Brunei's  method  at  Saltash,  England 306 

426  Pneumatic  caisson -308 

427  Pneumatic  caissons  at  L'Orient,  France 308 

428.  Pneumatic  caissons  at  St.  Louis,  Mo 310 

429.  Pneumatic  caissons  at  St.  Joseph,  Mo. 312 


CONTENTS. 


AHTIOLK 

430.  Pneumatic  caissons  at  New  York  City  ......................  314 

431.  Movable  pneumatic  caisson  ...............................  315 

433.  Securing  the  bed  of  the  foundation  from  injury  ...........  317 


PART  VI. 
CHAPTER  XIII.— BRIDGES. 

434          Definitions  and  classification 818 

435-436.  Component  parts  of  a  bridge 318 

437-441.  Piers  and  abutments,  fenders,  ice-breakers 319 

442-443.  Approaches . 325 

444.  The  frame  of  a  bridge  and  classification 327 

CHAPTER  XIV.— TRUSSED  BRIDGES. 

445.  Definitions 328 

446.  Systems 329 

447.  External  forces  acting  to  strain  the  bridge 329 

448.  Bang-post  truss 331 

449.  Fink's  truss 332 

450           Bollman's  truss 332 

451-453.  Method  of  determining  the  strains  on  a  triangular  truss 333 

454.  The  panel  system , 338 

455.  Queen-post  truss 339 

456-457.  The  bowstring  system 340 

458-459.  Compound  systems 344 

460.  Strains  produced  by  moving  loads 345 

461.  Counter-braces 346 

462.  Length  and  depth  of  a  truss 347 

463^72.  Description  of  the  "  graphical  method  " 347 

473.  Working,  proof,  and  breaking  loads 356 

474.  Wooden  bridge  trusses 356 

475.  Town's  truss. 357 

476.  Long's  truss 358 

477.  Burr's  truss 359 

479.  Canal  bridge  truss 360 

480.  Howe's  truss 360 

481.  Pratt's  truss 361 

488.          Bridge  trusses  of  iron 362 

484.  Continuity  of  the  truss 364 

CHAPTER  XV.— TUBULAR  AND  IRON  PLATE  BRIDGES. 

485.  Tubular  bridges 365 

486.  Iron  plate  bridges 367 

CHAPTER  XVI.— ARCHED  BRIDGES. 

487.  Form  of  arch  used  in  bridges 368 

488.  Masonry  arches — centres 369 

489-490.  Arched  bridges  of  iron— construction 370 

491.  Expansion  and  contraction 371 

492.  Arched  bridges  of  steel , 371 


CONTENTS. 


xiii 


IXTICXJE  PAGH 

493.  Ead's  patent  bridge 371 

494.  Circumstances  under  which  the  arch  may  be  pref  e'/red  to  the 

truss  in  a  bridge 372 

CHAPTER  XVII.—  SUSPENSION  BRIDGES. 

495-496.  Component  parts  of  a  suspension  bridge 373 

497.          Towers  for  suspension  bridges 373 

498-501.  Anchorages,  main  chains,  suspension  chains,  and  roadway. .  374 

502.  Oscillations  and  means  to  stiffen  a  bridge * ...  377 

503.  Suspension  railroad  bridge  over  Niagara  River 378 

504.  Suspension  bridge  over  tie  East  River,  New  York 381 

CHAPTER  XVHL— MOVABLE  AND  AQUEDUCT  BRIDGES. 

505-511.  Movable  bridges  and  classification 381 

512.  Aqueduct  bridges 383 

CHAPTER  XIX BRIDGE  CONSTRUCTION. 

513.  Necessary  things  to  be  considered  in  advance 884 

514-517.  Site,  water-way,  and  velocity  of  current 384 

518.          Design  of  bridge 387 

519-523.  Erection,  machinery  used,  modes  of  erection,  and  cost  of 

construction 388 


PART  VIL 


CHAPTER  XX.— ROOFS. 

524.  Definition  of  roof 390 

525-526.    Various  forms  of  roofs  and  kinds  of  coverings 390 

527.  Frames  used  to  support  a  roof 391 

528.  Remarks  upon  the  weights  resting  on  a  roof 391 

529-530.    Rise  and  span,  and  materials  used  in  construction  of  roofs.  392 

531.  King-post  roof  truss 393 

532.  Queen-post  roof  truss 394 

533.  Iron  roof  trusses 394 

534.  Determination  of  the  kind  and  amount  of  stresses  in  the 

pieces  of  a  king -post  truss 394 

535.  The  same  for  a  king-post  framed  with  struts 395 

536.  The  same  for  a  queen-post  truss 398 

537-538.    Strains    on  the  parts  of  an  iron  roof  truss  with  trussed 

rafters 398 

539.  Strains  on  the  parts  of  a  roof  truss,  the  rafters  of  which  are 

divided  into  three  parts,  and  are  supported  at  the  points 

of  division 403 

541-542.  Determination  by  the  graphical  method  of  the  stresses  in 

the  pieces  of  a  roof  truss 407 

543.  Purlins 409 

544.  Construction  of  roofs 409^ 


CONTENTS. 

PART  vm. 

CHAPTER  XXL—  ROADS. 


ABTZCLK 


PA01 


545.          Definition  of  a  road  .....................................  41C 

546!  Considerations  to  be  observed  in  laying  out  a  road  .........  411 

547_548.  Considerations  governing  the  choice  of  direction  of  the  road.  411 

549-551.  Grades  to  be  adopted  ....................................  412 

552-557.  Form  and  details  of  cross-section  .........................  413 

558.  Road-coverings  ..........................................  416 

559  Classification  of  ordinary  roads  from  the  kind  of  coverings 

used  ................................................  416 

560.  Earth  or  dirt  roads  ......................................  417 

561.  Corduroy  roads  .......................................    .  417 

562.  Plank  roads  ............................................  417 

563.  Gravel  roads  ............................................  418 

664.  Broken-stone  roads  ----  .  .................................  418 

565.  Macadamized  roads.  .  .    ,  ................................  419 

566,  Telford  roads  .........................................  419 

667.          Kinds  of  stone  used  in  broken-stone  roads  .................  420 

568.  Repairs  of  broken-stone  roads  ............................  420 

569.  Essential  qualities  of  a  paved  road  ........................  421 

570.  Roman  paved  roads  .....................................  421 

671.  English  paved  roads  ......  .  ..............................  421 

672.  Belgian  pavement  ......................................  422 

573.  Cobble-stone  pavement  .......  ...........................  423 

574.  Kinds  of  stone  suitable  for  paved  roads  .........   .........  423 

575.  Wooden  pavements  .....................................  423 

576.  Asphaltic  pavements  ....................................  424 

577.  Tram-roads  ............................................  424 

CHAPTER  XXII.—  LOCATION  AND  CONSTRUCTION  OF  ROADS. 

578.  Selection  of  route  .......................................  425 

579.  Reconnoissance  .........................................  425 

680.          Surveys  ................................................  427 

581-582.  Map,  memoir,  and  estimate  of  cost  .......................  427 

583-584.  Surveys  of  location  and  construction  ......................  429 

685-587.  Earthwork—  embankments,  etc  ...........................  430 

588.  Construction  in  swamps  and  marshes  .....................  433 

589.  Construction  of  side-hill  roads  ...........................  433 

590-594.  Drainage  of  roads  .......................................  435 

595-596.  Footpaths  and  sidewalks  ................................  437 

597-599  .  Construction  of  tram-roads  ..............  ----  438 


CHAPTER  XXIII. —RAILROADS. 

600.  Definition  of  railroad 439 

601.  Direction 430 

602.  Grades 440 

603.  Curves 441 

604-607.  Resistances  offered  to  traction  on  railroads 442 

608.          Formulas  for  total  resistance 443 

609-613.  Tractive  force  used  on  railroads 444 

614.  Gauge  of  railroads 444 

615-616.  Location  and  construction  of  railroads 446 

617-622.  Tunnels 44? 

623.          Ballast . .  45C 


CONTENTS.  XV 

ARTICU  PAGE 

624.  Cross-ties 450 

625.  Bails 450 

626.  Coning  of  wheels 451 

627.  Elevation  of  outer  rail  on  curves. 451 

628-630.  Crossings,  switches,  turn-tables,  etc 452 

CHAPTER  XXIV.— CANALS. 

681.  Definition  of  canal 453 

632-637.  Navigable  canals,  form,  construction,  and  size 453 

638-640.  Locks 457 

641.  Lock-gates 461 

642.  Inclined  planes 462 

643.  Guardlock 462 

644.  Lift  of  locks 462 

645-646.  Levels  and  water-supply 463 

648-650.  Feeders,  reservoirs,  dams,  and  waste-weirs 466 

651.  Water-courses  intersecting  the  line  of  the  canal 468 

652.  Dimensions  of  canals  and  locks  in  the  United  States 469 

653-655.  Irrigating  canals 469 

656.  Drainage  canals. 471 

657-658.  Canals  for  supplying  cities  and  towns  with  water 479 


INTRODUCTORY  CHAFIER. 


I.  Engineering  is  defined  to  be  "  the  science  and  art  of 
utilizing  the  forces  and  materials  of  nature." 

It  is  divided  into  two  principal  branches,  Civil  and  Military 
Engineering. 

The  latter  embraces  the  planning  and  construction  of  all  de- 
fensive and  offensive  works  used  in  military  operations. 

The  former  comprises  the  designing  and  building  of  all  works 
intended  for  the  comfort  of  man,  or  to  improve  the  country  either 
by  beautifying  it  or  increasing  its  prosperity. 

In  this  branch  the  constructions  are  divided  into  two  classes, 
according  as  the  parts  of  which  they  are  made  are  to  be  relatively 
at  rest  or  in  motion.  In  the  former  case  they  are  known  as 
structures,  and  in  the  latter  as  machines. 

II.  It  is  usual  to  limit  the  term  civil   engineering  to  the 
planning  and  construction  of  works  of  the  first  class,  and  to  use 
the  term  mechanical  or  dynamical  engineering  when  the 
works  considered  are  machines. 

It  is  also  usual  to  subdivide  civil  engineering  into  classes, 
according  to  the  prominence  given  to  some  one  or  more  of  its  parts 
when  applied  in  practice,  as  topographical  engineering,  hydraulic 
engineering,  railway  engineering,  etc.  By  these  divisions,  greater 
progress  toward  perfection  is  assured.  Notwithstanding  this  sepa- 
ration into  branches  and  subdivisions,  there  are  certain  general 
principles  common  to  them  all. 

HI.  The  object  of  the  following  pages  is  to  give  in  regular  order 
these  elementary  principles,  common  to  all  branches  of  engineering, 
which  the  student  should  learn,  so  that  he  may  understand  the 
nature  of  the  engineer's  profession,  and  know  how  to  apply  these 
principles  in  practice. 


XV111  INTRODUCTORY   CHAPTER. 

IV.  A  structure  is  a  combination  of  portions  of  solid  ma  eriais 
BO  arranged  as  to  withstand  the  action  of  any  external  for:es  to 
which  it  may  be  exposed,  and  still  to  preserve  its  form.     These 
portions  are  called  pieces,  and  the  surfaces  where  they  touch  and 
are  connected   are  called  joints.     The   term  solid  here  used  is 
applied  to  a  body  that  offers  an  appreciable  resistance  to  the  action 
of  the  different  forces  to  which  it  may  be  subjected. 

V.  That  part  of  the  solid  material  of  the  earth  upon  which  the 
structure  rests  is  called  the  foundation,  or  bed  of  the  founda- 
tion, of  the  structure. 

VI.  In  planning  and  building  a  structure,  the  engineer  should 
be  governed  by  the  following  conditions  : 

The  structure  should  possess  the  necessary  strength  ;  should 
last  the  required  time ;  and  its  cost  must  be  reasonable. 
In  other  words,  the  engineer  in  projecting  and  executing  a  work 
should  duly  consider  the  elements  of  strength,  durability,  and 
economy. 

VII.  The  permanence   of  a   structure   requires  that  it  should 
possess  stability,  strength,  and  stiffness.     It  will  possess  these 
when  the  following  conditions  are  fulfilled  : 

When  all  the  external  forces,  acting  on  the  whole  structure,  are 
in  equilibrium ; 

When  those,  acting  on  each  piece,  are  in  equilibrium  ; 

When  the  forces,  acting  on  each  of  the  parts  into  which  a  piece 
may  be  conceived  to  be  divided,  are  in  equilibrium  ;  and 

When  the  alteration  in  form  of  any  piece,  caused  by  the  exter- 
nal forces,  does  not  pass  certain  prescribed  limits. 

A  knowledge,  therefore,  of  the  forces  acting  on  the  structure, 
and  of  the  properties  of  the  materials  to  be  used  in  its  construc- 
tion, is  essential. 

VIII.  The  designing  and  building  of  a  structure  f.  rm  three  dis- 
tinct operations,  as  follows : 

1.  The  conception  of  the  project  or  plan ; 

2.  Putting  this  on  paper,  so  it  can  be  understood ,  and 

3.  Its  execution. 


INTEODUCTOKT   CHAPTER. 

The  first  requires  a  perfect  acquaintance  with  the  locality  whera 
the  structure  is  to  be  placed,  the  ends  or  objects  to  be  attained  by 
it,  and  the  kind  and  quantity  of  materials  that  can  be  supplied  at 
that  point  for  its  construction. 

The  second  requires  that  the  projector  should  know  something 
of  drawing,  as  it  is  only  by  drawings  and  models  accompanied  by 
descriptive  memoirs,  with  estimates  of  cost,  that  the  arrangement 
and  disposition  of  the  various  parts,  and  the  expense  of  a  proposed 
work,  can  be  understood  by  others. 

The  drawings  are  respectively  called  the  plan,  elevation,  and 
cross-section,  according  to  the  parts  they  represent.  A  sym- 
metrical structure  requires  but  few  drawings ;  one  not  symmetri- 
cal, or  having  different  fronts,  will  require  a  greater  number. 

These,  to  be  understood,  must  be  accompanied  by  written  speci- 
fications explaining  fully  all  the  parts. 

The  estimate  of  cost  is  based  upon  the  cost  of  the  materials,  the 
price  of  labor,  and  the  time  required  to  finish  the  work. 

The  third  may  be  divided  into  three  parts : 

1.  The  field-work,  or  laying  out  the  work ; 

2.  The  putting  together  the  materials  into  parts ;  and 

3.  The  combining  of  these  parts  in  the  structure. 

This  requires  a  knowledge  of  surveying,  levelling,  and  other 
operations  incident  to  laying  out  the  work ; 

A  knowledge  of  the  physical  properties  of  the  materials  used ; 

The  art  of  forming  them  into  the  shapes  required  ;  and 

How  they  should  be  joined  together  to  best  satisfy  the  condi- 
tions that  are  to  be  imposed  upon  the  structure. 


ELEMENTARY   COURSE 

OF 

CIVIL  ENGINEERING. 


PART    I. 


BUILDING  MATERIALS. 

1.  The  materials  in  general  use  by  civil  engineers  for  their 
constructions  may  be  arranged  in  three  classes : 

1st.  Those  which  constitute  the  more  solid  components  of 
structures ;  as  Wood,  Stone,  and  the  Metals. 

2d.  Those  which  unite  the  solid  parts  together;  as  Glue, 
Cements,  Mortars,  Mastics,  etc. 

3d.  Those  mixtures  and  chemical  preparations  which  are 
employed  to  protect  the  structure  from  the  action  of  the 
weather  and  other  causes  of  destructibility ;  as  Paints, 
Solutions  of  Salts,  Bituminous  Substances,  etc. 


CHAPTER  L 

WOOD. 

2.  The  abundance  and  cheapness  of  this  material  in  the 
United  States,  the  ease  with  which  it  could  be  procured  and 
worked,  and  its  strength,  lightness,  and  durability,  under 
favorable  circumstances,  have  caused  its  very  general  use  in 
every  class  of  constructions. 

Timber,  from  the  Saxon  word  timbrian,  to  build,  is  the 
term  applied  to  wood  of  a  suitable  size,  and  fit  for  building 
purposes.  While  in  the  tree  it  is  called  standing  timber; 
after  the  tree  is  felled,  the  portions  fit  for  building  are  cut 
into  proper  lengths  and  called  logs  or  rough  timber ;  when 
the  latter  have  been  squared  or  cut  into  shape,  either  to  be 


»r-*2*»**::  CIVIL   ENGINEERING. 


used  in  this  form  or  cut  into  smaller  pieces,  the  general  term 
timber  is  applied  to  them ;  if  from  the  trunk  of  the  tree, 
they  are  known  as  square  or  round,  hewn  or  sawed,  accord- 
ing to  the  form  of  cross-section  and  mode  of  cutting  it ;  if 
from  the  branches  or  roots,  and  of  crooked  shape,  they  are 
called  compass  timber.  The  latter  is  used  in  ship-building. 

The  logs,  being  sawed  into  smaller  pieces,  form  lumber, 
and  the  latter  is  divided  into  classes  known  as  joists,  scant- 
lings, strips,  boards,  planks,  etc.,  and,  when  sawed  to  suit  a 
given  bill ;  as  dimension  stuff. 

3.  The  trees  used  for  timber  are  exogenous — that  is,  they 
grow  or  increase  in  size  by  formation  of  new  wood  in  layers 
on  its  outer  surface. 

If  the  trunk  of  a  tree  is  cut  across  the  fibres,  the  cut  will 
show  a  series  of  consecutive  rings  or  layers. 

These  layers  are  of  annual  growth  in  the  temperate  zones, 
and,  by  counting  them,  the  approximate  age  of  the  tree  may 
be  determined. 

The  trunk  of  a  full-grown  tree  presents  three  distinct 
parts :  the  bark,  which  forms  the  exterior  coating ;  the  sap- 
wood,  which  is  next  to  the  bark ;  the  heart,  or  inner  part, 
which  is  easily  distinguishable  from  the  sap-wood  by  its 
greater  density,  hardness  and  strength,  'and  oftentimes  by  its 
darker  color. 

The  heart  embraces  essentially  all  that  part  of  the  trunk 
which  is  of  use  as  a  building  material.  The  sap-wood 
possesses  but  little  strength,  and  is  subject  to  rapid  decay, 
owing  to  the  great  quantity  of  fermentable  matter  contained 
in  it.  The  bark  is  not  only  without  strength,  but,  if  suffered 
to  remain  on  the  tree  after  it  is  felled,  it  hastens  the  decay  of 
the  sap-wood  and  heart. 


VARIETIES   OF   TIMBER-TREES   IN   THE   UNITED    STATES. 

4.  The  forests  of  our  own  country  produce  a  great  variety 
of  the  best  timber  for  every  purpose.  For  use  in  construc- 
tion, trees  are  divided  into  two  general  classes,  soft  wood, 
and  hard  wood  trees. 

The  first  includes  all  coniferous  trees,  like  the  pines,  and 
also  some  few  varieties  of  the  leaf- wood  trees;  and  the 
other  includes  most  of  the  timber  trees  that  are  non-conifer- 
ous, like  the  oaks,  etc. 

The  soft  wood  trees  generally  contain  turpentine,  and  are 
distinguished  by  straightness  of  fibre  and  by  the  regularity 
of  form  of  the  tree.  The  timber  made  from  them  is  more 


TIMBER.  3 

easily  sawed  or  split  along  the  grain,  and  much  more  easily 
broken  across  the  grain,  than  that  of  the  second  class. 

The  hard-wood,  or  non-coniferous  timber,  contains  no  tur- 
pentine, and,  as  a  class,  is  tough  and  strong. 

Examples  of  Soft-wood  Trees. 

5.  Yellow  Pine  (Pinus  mitis). — This  tree  is,  perhaps, 
in  this  country  the  most  widely  distributed  of  all  the  pines, 
being  found  in  all  the  States  from  New  England  to  the  Gulf 
of  Mexico.     In  the  Southern  States  it  is  called  the  Spruce 
Pine,  and  the  Short-leaved  Pine. 

The  heart-wood  is  fine  grained  and  moderately  resinous. 
Its  sap-wood  decays  rapidly  when  exposed  to  the  weather. 
The  tree  grows  mostly  in  light  clay  soils  and  furnishes  a 
strong  and  durable  timber  extensively  used  in  house  and 
ship  building. 

Long-leaf  Pine  (Pinus  australis). — This  tree  is  found 
from  southeastern  Virginia  to  the  Gulf,  and  is  the  principal 
tree  where  the  soil  is  sandy  and  dry.  Inferior  growths  of 
it  are  frequently  called  Yellow  Pine.  It  has  but  little 
sap-wood.  The  heart- wood  is  fine  grained,  compact,  and  has 
the  resinous  matter  very  uniformly  distributed. 

The  timber  made  from  it  is  strong  and  durable,  being 
considered  superior  to  that  of  the  other  pines.  Its  quality 
depends,  however,  on  the  kind  of  soil  in  which  the  tree 
grows,  being  less  resinous  in  rich  soils. 

Red  Pine  (Pinus  resinosa). — This  tree  is  found  in  Cana- 
da and  the  northwestern  parts  of  the  United  States,  and  is 
often  wrongly  called  "  Norway  Pine. "  It  furnishes  good, 
strong  and  durable  timber. 

White  Pine  (Pinus  strobus). — This  tree  is  found  in 
Canada  and  New  England,  and  along  the  Alleghanies  as  far 
south  as  Georgia,  and  frequently  called  Northern  Pine. 
Its  timber  is  light,  soft,  free  from  knots,  slightly  resinous, 
easily  worked,  and  durable  when  not  exposed  to  the  weath- 
er. It  is  used  in  a  great  variety  of  ways  for  building  pur- 
poses and  for  joiners'  work. 

6.  Fir. — The  genus  Fir  (Abies\  commonly  known  as 
Spruce,  furnishes  large  quantities  of  timber  and  lumber 
which  are  extensively  used  throughout  the  Northern  States. 
The  lumber  made  from  it  has  the  defects  of  twisting  and 
splitting  on  exposure  to  the  weather  and  of  decaying  rapidly 
in  damp  situations.     The  common  fir  (Abies  alba  and  Abies 
nigra),  the  spruce  fir  found  in  Northern  California,  and  the 


4  CIVIL   ENGINEERING. 

Oregon  fir  \_Pinus  (Abies)  Douglasii]  which  grows  to  an 
enormous  size,  all  furnish  timber  much  used  in  building. 

7.  Hemlock  (Abies  Canadensis)  is  a  well-known  species, 
used  throughout  the  Northern  States  as  a  substitute  for  pine 
when  the  latter  is  difficult  or  expensive  to  procure.     It  is 
very  perishable  in  damp  situations  or  when  subjected  to  alter- 
nate wetness  and  dryness.     It  has  been  used  in  considerable 
quantities  in  positions  where  it  is  entirely  submerged  in 
fresh   water.     Hemlock   timber  has   the  defects   of  being 
shaky,   full   of    knots,   and   more   difficult   to   work    than 
pine. 

8.  Cedar. — The  White  Cedar,  called  Juniper,  and  the 
Cypress  are  celebrated  for  furnishing  a  very  light  timber 
of  great  durability  when  exposed  to  the  weather;  on  this 
account  it  is  much   used  for  shingles   and  other  exterior 
coverings.     The  shingles  made  of  it  will  last,  so  it  is  said, 
for  40  years.     These  two  trees  are  found  in  great  abundance 
in  the  swamps  of  the  Southern  States. 

9.  The  foregoing  kinds  of  timber,  especially  the  pines,  are 
regarded  as  valuable  building  materials,  on  account  of  their 
strength,  their  durability,  the  straightness  of  the  fibre,  the 
ease  with  which  they  are  worked,  and  their  applicability  to 
almost  all  the  purposes  of  constructions  in  wood. 


Examples  of  Hard- wood  Trees. 

*10.  White  Oak  (Quercvs  alba). — The  bark  of  this  tree  is 
light,  nearly  white ;  the  leaf  is  long,  narrow,  and  deeply  in- 
dented ;  the  wood  is  compact,  tough,  and  pliable,  and  of  a 
straw  color  with  a  pinkish  tinge. 

It  is  largely  used  in  ship-building,  the  trunk  furnishing  the 
necessary  timber  for  the  heavy  frame- work,  and  the  roots  and 
large  branches  affording  an  excellent  quality  of  compass-tim- 
ber. Boards  made  from  it  are  liable  to  warp  and  crack. 
This  tree  grows  throughout  the  United  States  and  Canada,  but 
most  abundantly  in  the  Middle  States.  Proximity  to  salt  air 
during  the  growth  of  the  tree  appears  to  improve  the  quality 
of  the  timber.  The  character  of  the  soil  has  a  decided  effect 
on  it.  In  a  moist  soil,  the  tree  grows  to  a  larger  size,  but 
the  timber  loses  in  firmness  and  durability. 

Live  Oak  (Quercus  virens). — The  wood  of  this  tree  is  of 
a  yellowish  tinge ;  it  is  heavy,  compact,  and  of  a  fine  grain  ; 
it  is  stronger  and  more  durable  than  that  of  any  other  species, 
and  on  this  account  is  considered  invaluable  for  the  purposes 
of  ship-building,  for  which  it  has  been  exclusively  reserved, 


TIMBER.  5 

The  live  oak  is  not  found  farther  north  than  the  neighbor, 
hood  of  Norfolk,  Virginia,  nor  farther  inland  than  from  fif- 
teen to  twenty  miles  from  the  sea-coast. 

Post  Oak  (Quercus  obtusiloba). — This  tree  seldom  attains 
a  greater  diameter  than  about  fifteen  inches,  and  on  this 
account  is  mostly  used  for  posts,  from  which  use  it  takes  its 
name.  The  wood  has  a  yellowish  hue  and  close  grain ;  is  said 
to  exceed  white  oak  in  strength  and  durability,  and  is  there- 
fore an  excellent  building  material  for  the  lighter  kinds  of 
frame-work.  This  tree  is  found  most  abundantly  in  the 
forests  of  Maryland  and  Virginia,  and  is  there  frequently 
called  Box  White  Oak  and  Iron  Oak.  It  also  grows  in  the 
forests  of  the  Southern  and  Western  States,  but  is  rarely  seen 
farther  north  than  the  southern  part  of  New  York. 

Chestnut  White  Oak  (Quercus prinuspalustris). — This 
tree  is  abundant  from  North  Carolina  to  Florida.  The  tim- 
ber made  from  it  is  strong  and  durable,  but  inferior  to  that 
of  the  preceding  species. 

Water  Oak  (Quercus  aquaticd). — This  tree  gives  a  tough 
but  not  a  durable  timber.  It  grows  in  the  Southern  country 
from  Virginia  to  as  far  south  as  Georgia  and  Florida. 

Red  Oak  (Quercus  rubra). — This  tree  is  found  in  all  parts 
of  the  United  States.  The  wood  is  reddish,  of  a  coarse  tex- 
ture, and  quite  porous.  The  timber  made  from  it  is  gener- 
ally strong,  but  not  durable. 

11.  Black  Walnut  (Juglans  nigra). — The  timber  made 
from  this  tree  is  hard  and  fine-grained.     It  has  become  too 
valuable  to  be  used  in  building  purposes,  except  for  orna- 
mentation. 

Hickory  (Gary a  tomentosa). — The  wood  of  this  tree  is 
tough  and  flexible.  Its  great  heaviness  and  liability  to  be 
worm-eaten  have  prevented  its  general  use  in  buildings. 

12.  There  are  a  number  of  other  trees,  belonging  to  both 
hard  and  soft  woods,  that  produce  timber  inferior  to  those 
named.     They  may  possibly  in  the  future  be  used  to  some 
extent  to  furnish  timber  for  building  purposes.     The  Red 
Cedar,  Chestnut,  Ash,  Elm,  Poplar,  American  Lime  or  Bass- 
wood,  Beech,  Sycamore,  Tamarack,  etc.,  have  all  been  used 
to  a  limited  extent  in  constructions  when  the  other  kinds 
were  not  to  be  obtained. 


PREPAEATION  OF  TIMBER. 

13.  Felling. — Trees  should  not  be  felled  for  timber  until 
they  have  attained  their  mature  growth,  nor  after  they  ex- 


6  CIVIL   ENGINEERING. 

hibit  symptoms  of  decline ;  otherwise  the  timber  will  not  pos- 
sess its  maximum  strength  and  durability.  Most  forest  treea 
arrive  at  maturity  in  between  fifty  and  one  hundred  years, 
and  commence  to  decline  after  one  hundred  and  fifty  or  two 
hundred  years.  When  a  tree  commences  to  decline,  the 
extremities  of  its  older  branches,  and  particularly  its  top, 
exhibit  signs  of  decay.  The  age  of  a  tree  can,  in  most  cases, 
be  approximately  ascertained  either  by  its  external  appear- 
ances or  by  cutting  into  the  centre  of  its  trunk  and  counting 
the  rings  or  layers  of  the  sap  and  heart. 

Trees  should  not  be  felled  while  the  sap  is  in  circulation ; 
for  this  substance  is  of  such  peculiarly  fermentable  nature, 
that  if  allowed  to  remain  in  the  fallen  timber,  it  is  very  pro- 
ductive of  destruction  of  the  wood.  The  best  authorities  on 
the  subject  agree  that  the  tree  should  be  felled  in  the  -win- 
ter season. 

The  practice  in  the  United  States  accords  with  the  above, 
not  so  much  on  account  of  the  sap  not  being  in  circulation, 
as  for  the  reason  that  the  winter  season  is  the  best'  time  for 
procuring  the  necessary  labor,  and  the  most  favorable  for  re- 
moving the  logs,  from  where  they  are  cut,  to  the  points  where 
they  are  to  be  made  into  rafts. 

As  soon  as  the  tree  is  felled,  it  should  be  stripped  of  its 
bark  and  raised  from  the  ground.  A  short  time  only  should 
elapse  before  the  sap-wood  is  taken  off  and  the  timber  reduced 
nearly  to  its  required  dimensions. 

14:.  Measuring-  Timber. — Timber  is  measured  by  the 
cubic  foot,  or  by  board  measure  /  the  unit  of  the  latter  is  a 
board  one  foot  square  and  one  inch  thick. 


Appearances  of  Good  Timber. 

15.  Among  trees  of  the  same  species,  that  one  which  has 
grown  the  slowest,  as  shown  by  the  narrowness  of  its  annual 
rings,  will  in  general  be  the  strongest  and  most  durable. 

The  grain  should  be  hard  and  compact,  and  if  a  cut  be 
made  across  it,  the  fresh  surface  of  the  cut  should  be  iirm  and 
shining. 

And,  in  general,  other  conditions  being  the  same,  the 
strength  and  durability  of  timber  will  increase  with  its  weight, 
and  darkness  of  color. 

Timber  of  good  quality  should  be  straight-grained,  and 
free  from  knots.  It  should  be  free  f rom  all  blemishes  and 
defects. 


TIMBER. 


Defects  in  Timber. 

16.  Defects  arise  from  some  peculiarity  in  the  growth  of 
the  tree,  or  from  the  effects  of  the  weather. 

Strong  winds  oftentimes  injure  the  growing  tree  by  twist- 
ing or  bending  it  so  as  to  partially  separate  one  annual  layer 
from  another,  forming  what  is  known  as  rolled  timber  or 
shakes. 

Severe  frosts  sometimes  cause  cracks  radiating  from  the 
centre  to  the  surface. 

These  defects,  as  well  as  those  arising  from  worms  or  age, 
may  be  detected  by  examining  a  cross-section  of  the  log. 


SEASONING   OF   TIMBER. 

17.  Timber  is  said  to  be  seasoned  when  by  some  process, 
either  natural  or  artificial,  the  moisture  in  it  has  been  ex- 
pelled so  far  as  to  prevent  decay  from  internal  causes. 

The  term  seasoning  means  not  only  the  drying  of  the 
timber,  but  also  the  removal  or  change  of  the  albuminous  sub- 
stances in  it.  These  substances  are  fermentable,  and  when 
present  unchanged  in  the  timber  are  ever  ready  to  promote 
decay. 

The  seasoning  of  timber  is  of  the  greatest  importance,  not 
only  to  its  own  durability,  but  to  the  solidity  of  the  structure 
for  which  it  may  be  used ;  for,  if  the  latter,  when  erected, 
contained  some  pieces  of  unseasoned  or  green  timber,  their 
after-shrinking  might,  in  many  cases,  cause  material  injury, 
if  not  complete  destruction,  to  the  structure. 

Natural  Seasoning  consists  in  exposing  the  timber  freely 
to  the  air,  but  in  a  dry  place,  sheltered  from  the  sun  and  high 
winds. 

This  method  is  preferable  to  any  other,  as  timber  seasoned 
in  this  way  is  both  stronger  and  more  durable  than  when  pre- 
pared by  any  artificial  process.  It  will  require,  on  an  aver- 
age, about  two  years  to  season  timber  thoroughly  by  this 
method.  For  this  reason,  artificial  methods  are  used  to  save 
time. 

Water  Seasoning. — The  simplest  artificial  method  con- 
sists in  immersing  the  timber  in  water  as  soon  as  cut, 
taking  care  to  keep  it  entirely  submerged  for  a  fortnight, 
and  then  to  remove  it  to  a  suitable  place  and  dry  it. 
The  water  will  remove  the  greater  portion  of  the  sap, 
even  if  the  timber  is  full  when  immersed.  This  method 
doubtless  weakens  the  timber  to  some  extent,  and  therefore 


g  CIVIL   ENGINEERING. 

is  not  recommended  where  strength  in  the  timber  is  the 
most  important  quality. 

Boiling  and  Steaming  have  both  been  used  for  seasoning 
but  are  open  to  the  same  objection  as  the  last  method  ;  viz... 
the  impairing  of  the  elasticity  and  strength  of  the  timber. 

Hot-air  Process. — This  consists  in  exposing  the  timber  in 
a  chamber,  or  oven,  to  a  current  of  hot  air,  whose  temperature 
varies  according  to  the  kind  and  size  of  the  timber  to  be  sea- 
soned. This  is  considered  the  best  of  the  artificial  methods. 
The  time  required  for  sufficient  seasoning  depends  upon  the 
thickness  of  the  timber,  ordinary  lumber  requiring  from  one 
to  ten  weeks. 


DURABILITY   AND   DECAY   OF   TIMBER. 

18.  Timber  lasts  best  when  kept,  or  used,  in  a  dry  and 
well-ventilated  place.  Its  durability  depends  upon  its  pro- 
tection from  decay  and  from  the  attacks  of  worms  and  insects. 

The  wet  and  dry  rot  are  the  most  serious  causes  of  the 
decay  of  timber. 

Wet  Rot  is  a  slow  combustion,  a  decomposition  of  moist 
organic  matter  exposed  to  the  air,  without  sensible  elevation 
of  temperature.  The  decay  from  wet  rot  is  communicated 
by  contact,  and  requires  the  presence  of  moisture. 

To  guard  against  this  kind  of  rot,  the  timber  must  not  be 
subjected  to  a  condition  of  alternate  wetness  and  dryness,  or 
even  to  a  slight  degree  of  moisture  if  accompanied  by  heat 
and  confined  air. 

Dry  Rot  is  a  decay  arising  from  the  decomposition  of  the 
fermentable  substances  in  the  timber;  it  is  accompanied  by 
the  growth  of  a  fungus,  whose  germs  spread  in  all  directions, 
finally  converting  the  wood  into  a  fine  powder.  The  fungus 
is  not  the  cause  of  decay ;  it  is  only  a  morbid  growth  due  to 
the  decaying  fibres  of  the  wood. 

Dry  rot  derives  its  name  from  the  effect  produced  and  not 
from  the  cause,  and  although  it  is  usually  generated  in  moist- 
ure, it  is  frequently  found  to  be  independent  of  extraneous 
humidity.  Externally,  it  makes  its  first  appearance  as  a  mil- 
dew, or  a  white  or  yellowish  vegetation  of  like  appearance. 
An  examination  under  a  microscope  of  a  section  of  apiece  of 
wood  attacked  by  dry  rot  shows  minute  white  threads  spread- 
ing and  ramifying  throughout  the  substance. 

Dry  rot  only  attacks  wood  which  is  dead,  whereas  wet 
rot  may  seize  the  tree  while  it  is  still  alive  and  standing. 
Timber,  not  properly  seasoned,  used  where  there  is  a  want 


TIMBER.  9 


of  free  circulation  of  air,  decays  by  dry  rot  even  if  there  be 
only  a  small  amount  of  moisture  present.  It  will  also  decay 
by  dry  rot,  if  covered  while  unseasoned  by  a  coat  of  paint,  or 
similar  substance. 


Durability  under  certain  Conditions,  and  Means  of  In« 
creasing  it. 

19.  Timber  may  be  subjected  to  the  following  conditions : 

It  may  be  kept  constantly  dry,  or  at  least  practically  so 

It  may  be  kept  constantly  -wet  in  fresh  water. 

It  may  be  constantly  damp. 

It  may  be  alternately  wet  and  dry. 

It  may  be  constantly  wet  in  sea-water. 

20.  Timber  kept  constantly  dry  in  well-ventilated  posi- 
tions, will  last  for  centuries.     The  roof  of  Westminster  Hall 
is  more  than  450  years  old.     In  Stirling  Castle  are  carvings 
in  oak,  well  preserved,  over  300  years  old ;  and  the  trusses  of 
the  roof  of  the  Basilica  of  St.  Paul,  Rome,  were  sound  and 
good  after  1000  years  of  service.      The  timber  dome  of  St. 
Mark,  at  Venice,  was  in  good  condition  850  years  after  it  was 
built. 

It  would  seem  hardly  worth  while  to  attempt  to  increase 
the  durability  of  timber  when  under  these  conditions,  except 
where  it  may  be  necessary  to  guard  against  the  attacks  of  in- 
sects, which  are  very  destructive  in  some  localities.  Damp 
lime  hastens  the  decay  of  timber  ;  the  latter  should  therefore, 
in  buildings,  be  protected  against  contact  with  the  mortar. 

21 .  Timber  kept  constantly  wet  in  fresh  water,  under 
such  conditions  as  will  exclude  the  air,  is  also  very  durable. 

Oak,  elm,  beach,  and  chestnut  piles  and  planks  were  found 
beneath  the  foundation  of  Savoy  Place,  London,  in  a  perfect 
state  of  preservation,  after  having  been  there  650  years. 

The  piles  of  the  old  London  Bridge  were  sound  800  years 
after  they  were  driven.  In  the  bridge  built  by  Trajan,  the 
piles,  after  being  driven  more  than  1600  years,  were  found  to 
have  a  hard  exterior,  similar  to  a  petrifaction,  for  about  four 
inches,  the  rest  of  the  wood  being  in  its  ordinary  condition. 

We  may  conclude  that  timber  submerged  in  fresh  water 
will  need  no  artificial  aid  to  increase  its  durability,  although  in 
time  it  may  be  somewhat  softened  and  weakened. 

22.  Timber  in  damp  situations. — Timber  in  damp  sit- 
uations is  in  a  place  very  unfavorable  for  durability,  and  is 
liable,  as  previously  stated,  to  decay  rapidly.     In  such  situa- 


10  CIVIL   ENGINEERING. 

tions  only  the  most  lasting  material  is  to  be  employed,  and 
every  precaution  should  be  taken  to  increase  its  durability. 

23.  Timber  alternately  wet  and  dry. — The  surface  of 
all  timber  exposed  to  alternations  of  wetness  and  dry  ness 
gradually  wastes  away,  becoming  dark-colored  or  black. '  This 
is  wet  rot,  or  simply  " rot" 

Density  and  resinousness  exclude  moisture  to  a  great  ex- 
tent; hence  timber  possessing  these  qualities  should  be  used 
in  such  situations.  Heart-wood,  from  its  superior  density,  is 
more  durable  than  sap-wood ;  oak,  than  poplar  or  willow. 
Resinous  wood,  as  pine,  is  more  durable  than  the  non-resin- 
ous, as  ash  or  beech,  in  such  situations. 

24.  Timber  constantly  wet  in  sea-water. — The  re- 
marks made  about  timber  placed  in  fresh  water  apply  equally 
to  this  case,  as  far    as   relate    to  decay  from  rot.     Timber 
immersed  in  salt  water  is,  however,  liable  to  the  attacks  of  tw,o 
of  the  destructive  inhabitants  of  our  waters,  the  Limnoria 
terebrans  and  Teredo  navalis  ;  the  former  rapidly  de- 
stroys the  heaviest  logs  by  gradually  eating  in  between  the 
annual  rings ;  and  the  latter,  the  well-known  ship-worm,  con- 
verts timber  into  a  perfectly  honeycombed  state  by  its  nu- 
merous perforations.  They  both  attack  timber  from  the  level 
of  the  mud,  or  bottom  of  the  water,  and  work  to  a  height 
slightly  above  mean  low  water.     The  timber,  for  this  dis- 
tance, must  be  protected  by  sheathing  it  with  copper,  or  by 
thickly  studding  the  surface  with  broad-headed  iron  nails,  or 
other  similar  device.     Resinous  woods  resist  their  attacks 
longer,  most  probably  on  account  of  the  resin  in  the  wood. 
The  resin  after  a  time  is  washed  or  dissolved  out,  and  the 
timber  is  then  speedily  attacked. 

An  examination  of'  piles  in  the  wharf  at  Fort  Point,  San 
Francisco  harbor,  where  these  agents  are  very  destructive, 
showed  that  piles  which  were  driven  without  removing  the 
bark,  resisted  to  a  certain  extent,  their  destructive  attacks. 

Timber  saturated  with  dead  oil  by  the  process  known  as 
creosoting  is  said  to  offer  an  effective  resistance. 


PRESERVATION  OF  TIMBER. 

25.  The  necessity  of  putting  timber  into  damp  places  has 
caused  numerous  experiments  to  be  made  as  to  the  best 
method  of  increasing  its  durability  under  such  circumstances. 

There  are  three  means  which  may  be  used  to  increase  the 
durability  of  timber  placed  in  damp  situations,  viz : 


TIMBER.  11 

1st  To  season  it  thoroughly. 

2d.  To  keep  a  constant  circulation  of  air  about  it. 

3d.  To  cover  it  with  a  preservative. 

The  cellulose  matter  of  the  woody  fibre  is  very  durable 
when  not  acted  upon  by  fermentation,  and  the  object  of  sea- 
soning is  to  remove  or  change  the  fermentable  substances,  as 
well  as  to  expel  the  moisture  in  the  timber,  thus  protecting 
the  cellulose  portion  from  decay.  Even  if  the  timber  be 
well  seasoned,  thorough  ventilation  is  indispensable  in  damp 
situations.  The  rapid  decay  of  sills  and  lower  floors  is  not 
surprising  where  there  are  neither  wall-gratings  nor  venti- 
lating flues  to  carry  off  the  moisture  and  the  foul  gases  rising 
from  the  earth  under  them.  The  lower  floors  would  last 
nearly  as  long  as  the  upper  ones  if  the  earth  were  removed 
to  the  bottom  of  the  foundation  and  the  space  filled  in  with 
dry  material,  as  sand,  plaster,  rubbish,  etc.,  or  the  bottom 
covered  with  a  concrete  floor  to  exclude  the  moisture,  and 
arrangements  made  to  allow  a  free  circulation  of  air  under 
the  sills. 

An  external  coating  of  paint,  pitch,  or  hot  oil  increases 
the  durability  of  well-seasoned  timber,  but  such  a  coating 
upon  the  surface  of  green  timber  produces  just  the  opposite 
effect.  The  coating  of  paint  closes  the  pores  of  the  outer 
surface,  and  prevents  the  escape  of  the  moisture  from  with- 
in, thus  retaining  in  the  wood  the  elements  of  decay. 

It  is  not  always  practicable  to  employ  the  foregoing  means 
in  damp  places  to  preserve  the  timber,  and  other  methods 
have  to  be  used.  These  methods  are  based  upon  the 
principle  of  expelling  the  albuminous  substances  and  replac- 
ing them  by  others  of  a  durable  nature,  or  on  that  of  chang- 
ing the  albuminous  substances  into  insoluble  compounds  by 
saturating  the  timber  with  salts  of  an  earthy  or  metallic  base 
which  will  combine  with  the  albuminous  matter  and  make 
it  inert. 

Some  of  the  methods  which  have  been  proposed,  or  used, 
are  as  follows : 

Kyanizing. — Kyan's  method  is  to  saturate  the  timber 
with  a  solution  of  mercuric  chloride,  one  pound  of  chloride 
to  four  gallons  of  water. 

The  complete  injection  of  the  liquid  is  obtained  either  by 
long  immersion  in  the  liquid  in  open  vats,  or  by  great  pres- 
sure upon  both  solution  and  wood  in  large  wrought-iron 
tanks. 

The  expensiveness  of  the  process,  and  its  unhealthiness 
to  those  employed  in  it,  forbid  its  extensive  use. 


12  CIVIL  ENGINEEKING. 

Burnettizing.— Burnett's  process  is  to  use  a  solution  of 
chloride  of  zinc,  one  pound  of  the  chloride  to  ten  gallons  of 
water;  the  solution  being  forced  into  the  wood  under  a  pres- 
sure of  150  pounds  to  the  square  inch. 

Earle's  Process  consisted  in  boiling  the  timber  in  a  solu- 
tion of  one  part  of  sulphate  of  copper  to  three  parts  of  the 
sulphate  of  iron ;  one  gallon  of  water  being  used  with  every 
pound  of  the  salts.  A  hole  was  bored  ^through  the  whole 
length  of  the  piece ;  the  timber  was  then  immersed  from  two 
to  TOUT  hours,  and  allowed  to  cool  in  the  mixture. 

Ringold  and  Earle  invented  the  following  process :  A  hole 
from  -J  to  2  inches  in  diameter  was  made  the  whole  length  of 
the  piece,  and  the  timber  boiled  from  two  to  four  hours  in 
lime-water.  After  the  piece  was  dried,  the  hole  was  filled  with 
lime  and  coal-tar.  Neither  of  the  last  two  methods  was  very 
successful. 

Common  Salt  is  known  in  many  cases  to  be  a  good 
preservative.  According  to  Mr.  Bates's  opinion  this  method 
often  answers  a  good  purpose  if  the  pieces  so  treated  are 
not  too  large. 

Boucherie's  Process  employs  a  solution  of  sulphate  of  cop- 
per or  pyrolignite  of  iron.  One  end  of  the  green  stick  is  en- 
closed in  a  close-fitting  collar,  to  which  is  attached  a  water- 
tight bag  communicating  through  a  flexible  tube  with  an 
elevated  reservoir  containing  the  solution.  Hydrostatic  pres- 
sure soon  expels  the  sap.  When  the  solution  issues  in  a  pure 
state  from  the  opposite  end  of  the  log,  the  process  is  complete. 

It  was  found  that  the  fluid  will  pass  a  distance  of  twelve 
feet  along  the  grain  under  less  pressure  than  is  necessary  to 
force  it  across  the  grain  three-fourths  of  an  inch.  The  opera- 
tion is  performed  upon  green  timber  with  great  facility. 

In  1846,  80,000  railroad  ties  of  the  most  perishable  woods, 
impregnated,  by  Boucherie's  process,  with  sulphate  of  copper, 
were  laid  down  on  French  railways.  After  nine  years'  expo- 
sure they  were  found  as  perfect  as  when  laid.  This  experi 
ment  was  so  satisfactory  that  most  of  the  railways  of  that 
country  at  once  adopted  the  process.  It  has  been  suggested 
to  wash  out  the  sap  with  water,  which  would  not  coagulate 
the  albumen,  and  then  to  use  the  solution. 

Bethel's  Process. — The  timber  is  placed  in  an  air-tight 
cylinder  of  boiler-iron,  and  the  air  partially  exhausted.  Dead 
oil  is  then  admitted  at  a  temperature  of  120°  Fahr.,  and  a 
pressure  of  about  150  pounds  to  the  square  inch  is  then  ap 
plied,  and  maintained  from  five  to  eight  hours,  according  to 
the  size  of  the  timbers  under  treatment.  The  oil  is  then 
drawn  off,  and  the  timber  is  removed. 


STONE.  13 

The  Seeley  Process  consists  in  subjecting  the  wood,  while 
immersed  in  dead  oil,  to  a  temperature  between  212°  and 
300°  Fahr.  for  a  sufficient  length  of  time  to  expel  any  mois- 
ture present ;  the  water  being  expelled,  the  hot  oil  is  quickly 
replaced  by  cold,  thus  condensing  the  steam  in  the  pores  of 
the  timber,  forming  a  vacuum  into  which  oil  is  forced  by  at- 
mospheric pressure  and  capillary  attraction.  In  this  process 
from  six  to  twelve  pounds  of  oil  is  expended  for  each  cubic 
foot  of  wood. 

The  theory  of  this  process  is  that  the  first  part  of  the  opera- 
tion seasons  the  wood,  destroys  or  coagulates  the  albumen, 
and  expels  the  moisture ;  and  that  the  second  part  fills  the 
wood-cells  with  a  material  that  is  an  antiseptic  and  resists  de- 
structive agents  of  every  kind. 

Robbins's  Process  consists  in  treating  timber  with  coal-tar 
in  the  form  of  vapor. 

The  wood  is  placed  in  an  air-tight  iron  chamber,  with 
which  is  connected  a  still  or  retort,  over  a  furnace.  The  fur- 
nace is  then  fired  and  the  wood  kept  exposed  to  the  heated 
vapors  of  the  coal  tar  from  six  to  twelve  hours  ;  the  operation 
is  then  considered  complete. 

The  most  improved  of  all  these  methods  is  Seeley's ;  thig 
is  a  modification  and  an  improvement  of  Bethel's  process,  and 
is  generally  known  as  "  creosoting." 

It  is  thought  that  the  ancient  Egyptians  knew  of  some  pro- 
cess of  preserving  wood.  Old  cases,  supposed  to  have  been 
2,000  years  old,  apparently  of  sycamore  impregnated  with 
bitumen,  have  been  found  to  be  still  perfectly  sound  and 
strong. 


CHAPTER  IL 
STONE. 

26.  The  qualities  required  in  stone  for  building  purposes 
are  so  various  that  no  very  precise  directions  can  be  given  to 
exactly  meet  any  particular  case.  What  would  be  required 
for  a  sea-wall  would  not  be  suited  to  a  dwelling-house.  In 
most  cases  the  choice  is  limited  by  the  cost.  The  most 
essential  properties  of  stone  as  a  building  material  are 
strength,  hardness,  durability,  and  ease  of  working. 
These  properties  are  determined  by  experience  or  actual 
experiment. 


14  CIVIL   ENGINEERING. 

27.  The  term  Stone,  or  Rock,  is  applied  to  any  aggregation 
of  several  mineral  substances ;  as  a  building  material,  stones 
may  be  either  natural  or  artificial. 

Natural  Stones  may  be  subdivided  into  three  classes ;  the 
silicious,  the  argillaceous,  and  the  calcareous,  according  as 
silica,  clay,  or  lime  is  the  principal  constituent. 

Artificial  Stones  are  imitations  of  natural  stone,  made  by 
consolidating  fragmentary  solid  material  by  various  means; 
they  may  be  subdivided  into  classes  as  follows: 

1st.  Those  in  which  two  or  more  kinds  of  solid  materials 
are  mixed  together  and  consolidated  by  baking  or  burning ; 
as  brick,  tiles,  etc. 

2d.  Those  in  which  the  solid  materials  are  mixed  with 
some  fluid  or  semi-fluid  substance,  which  latter,  hardening 
afterwards  by  chemical  combinations,  binds  the  former  firmly 
together;  as  ordinary  concrete,  patent  stone,  etc. 

3d.  Those  in  which  the  solid  materials  are  mixed  with 
some  hot  fluid  substance  which  hardens  upon  cooling ;  as 
asphaltic  concrete,  etc. 


I.  NATURAL  STONES. 

GENERAL    OBSERVATIONS    ON    THE     PROPERTIES    OF    STONE    AS    A 
BUILDING   MATERIAL. 

28.  Strength,  hardness,  durability,  and  ease  of  working 
have  already  been  mentioned   as  essential  properties  to  be 
considered  in  selecting  stone  for  building  purposes. 

It  is  not  easy  to  judge  of  the  qualities  from  external 
appearances.  In  most  cases  stone,  which  has  one  of  the 
three  properties  first  named,  will  have  also  the  other  two.  In 
general,  when  the  texture  is  uniform  and  compact,  the  grain 
fine,  the  color  dark,  and  the  specific  gravity  great,  the  stone 
is  of  good  quality.  If  there  are  cracks,  cavities,  presence 
of  iron,  etc.,  even  though  it  belong  to  a  good  class  of  stone,  it 
will  be  deficient  in  some  of  these  essential  qualities,  and 
should  be  rejected.  A  coarse  stone  is  ordinarily  brittle,  and 
is  difficult  to  work ;  it  is  also  more  liable  to  disintegrate  than 
that  of  a  finer  grain. 

29.  Strength. — Among  stones  of  the  same  kind,  the  strong- 
est is  almost  always  that  which  has  the  greatest  heaviness. 

As  stone  is  ordinarily  to  be  subjected  only  to  a  crushing  force, 
it  will  only  be  in  particular  cases  that  the  resistance  to  this 
strain  need  be  considered,  the  strength  of  stone  in  this  respect 
being  greater  than  is  generally  required  of  it.  If  its  dura- 


STONE.  15 

bility  is  satisfactorily  proved,  its  strength,  as  a  rule,  may  be 
assumed  to  be  sufficient. 

30.  Hardness. — This    property  is  easily   ascertained   by 
actual  experiment  and  by  a  comparison  made  with  other 
stones  which  have  been  tested.     It  is  an  essential  quality  in 
stone  exposed  to  wear  by  attrition.     Stone  selected  for  paving, 
flagging  and  for  stairs,  should  be  hard  and  of  a  grain  too 
coarse  to  admit  of  becoming  very  smooth  under  the  action  to 
which  it  is  submitted. 

By  the  absorption  of  water,  stones  become  softer  and  more 
friable. 

31.  Durability. — By  this  term  is. meant  the  power  to  resist 
the  wear  and  tear  of  atmospheric  agencies,  the  capacity  to 
sustain  high  temperature,  and  the  ability  to  resist  the  destruc- 
tive action  of  fresh  and  salt  water. 

The  appearances  which  indicate  probable  durability  are 
often  deceptive. 

As  a  general  rule,  among  stones  of  the  same  kind,  those 
which  are  fine-grained,  absorb  least  water,  and  are  of  greatest 
specific  gravity,  are  also  most  durable  under  ordinary  expo- 
sures. The  weight  of  a  stone,  however,  may  arise  from  a 
large  proportion  of  metallic  oxide — a  circumstance  often  un- 
favorable to  durability. 

The  various  chemical  combinations  of  iron,  potash,  and 
alumina,  when  found  in  considerable  quantities  in  the  sili- 
cious  rocks,  greatly  affect  their  durability.  The  decompo- 
sition of  the  feldspar  by  which  a  considerable  portion  of  the 
silica  is  removed  when  the  potash  dissolves,  leaves  an  excess 
of  aluminous  matter  behind.  The  clay  often  absorbs  water, 
becomes  soft,  and  causes  the  stone  to  crumble  to  pieces. 

32.  Frost,  or  rather  the  alternate  action  of  freezing  and 
thawing,  is  the  most  destructive  agent  of  nature  with  which 
the  engineer  has  to  contend.     Its  effects  vary  with  the  tex- 
ture of  stones ;  those  of  a  fissile  nature  usually  split,  while 
the  more  porous  kinds  disintegrate,  or  exfoliate  at  the  surface. 
When  stone  from  a  new  quarry  is  to  be  tried,  the  best  indi- 
cation of  its  resistance  to  frost  may  be  obtained  from  an  ex- 
amination of  any  rocks  of  the  same  kind,  within  its  vicinity, 
which  are  known  to  have  been  exposed  for  a  long  period. 
Submitting  the  stone  fresh  from  the.  quarry  to  the   direct 
action  of  freezing  would  seem  to  be  the  best  test  of  it,  if  it 
were  not  that  there  are  some  kinds  of  stone  that  are  much 
affected  by  frost  when  they  are  first  quarried  due  to  the 
moisture  present  in   the  stone,  which  moisture   is  lost   by 
exposure  to  the  air,  and  is  never  reabsorbed  to  the  same 
amount. 


16  CIVIL   ENGINEERING. 

A  test  for  ascertaining  the  probable  effects  of  frost  on 
stone  was  invented  by  M.  Brard,  a  French  chemist,  and  may 
be  used  for  determining  the  probable  comparative  durabili- 
ties of  specimens.  It  imitates  the  disintegrating  action  of 
frost  by  means  of  the  crystallization  of  sodium  sulphate.  The 
process  may  be  stated  briefly  as  follows :  Let  a  cubical  block, 
about  two  inches  on  the  edge,  be  carefully  sawed  from  the 
stone  to  be  tested.  A  cold  saturated  solution  of  the  sodium 
sulphate  is  prepared,  placed  over  a  fire,  and  brought  to  the 
boiling-point.  The  stone,  having  been  weighed,  is  suspended 
from  a  string,  and  immersed  in  the  boiling  liquid  for  thirty 
minutes.  It  is  then  carefully  withdrawn,  the  liquid  is  de- 
canted free  from  sediment  into  a  flat  vessel,  and  the  stone  is 
suspended  over  it  in  a  cool  cellar.  An  efflorescence  of  the 
salt  soon  makes  its  appearance  on  the  stone,  when  it  must  be 
again  dipped  in  the  liquid.  This  should  be  frequently  done 
during  the  day,  and  the  process  be  continued  for  about  a 
week.  The  earthy  sediment  found  at  the  end  of  this  period 
in  the  vessel  is  carefully  weighed,  and  its  quantity  will  give 
an  indication  of  the  like  effect  of  frost.  This  process  is 
given  in  detail  in  Yol.  XXXVIII.  Annales  de  Chemie  et  de 
Physique. 

This  test,  having  corresponded  closely  with  their  experi- 
ence, has  received  the  approval  of  many  French  architects 
and  engineers.  Experiments,  however,  made  by  English  engi- 
neers on  some  of  the  more  porous  stones,  by  exposing  them 
to  the  alternate  action  of  freezing  and  thawing,  gave  results 
very  different  from  those  obtained  by  Brard's  method. 

33.  The  Wear  of  Stone  from  ordinary  exposure  is  very 
variable,  depending  not  only  upon  the  texture  and  constituent 
elements  of  the  stone,  but  also  upon  the  locality,  and  the  posi- 
tion, it  may  occupy  in  a  structure,  with  respect  to  the  pre- 
vailing driving  rains.  This  influence  of  locality  on  the 
durability  of  stone  is  very  marked.  Stone  is  observed  to  wear 
more  rapidly  in  cities  than  in  the  country,  and  exhibits  signs 
of  decay  soonest  in  those  parts  of  a  building  exposed  to  the 
prevailing  winds  and  rains. 

The  disintegration  of  the  stratified  stones  placed  in  a  wall 
is  materially  affected  by  the  position  of  the  strata  or  laminae 
with  respect  to  the  exposed  surface,  proceeding  faster  when 
the  faces  of  the  strata  are  exposed,  as  is  the  case  when  the 
stones  are  not  placed  with  their  laminae  lying  horizontally. 

Stones  are  often  exposed  to  the  action  of  high  temperatures, 
as  in  the  case  of  great  conflagrations.  They  are  also  used  to 
protect  portions  or  a  building  from  great  heat,  and  sometimes 
to  line  furnaces.  Those  that  resist  a  high  degree  of  heat  are 


STONE.  17 

termed  fire- stones.  A  good  fire-stone  should  be  infusible, 
and  not  liable  to  crack  or  exfoliate  from  heat.  Stones  that 
contain  lime  or  magnesia  are  usually  unsuitable.  Also,  sili- 
cates containing  an  oxide  of  iron. 

Their  durability  under  such  circumstances  should  be  con- 
sidered when  selecting  them  for  building. 

The  only  sure  test,  however,  of  the  durability  of  any  kind 
of  stone  is  its  wear,  as  shown  by  experience. 

34.  Expansion  of  Stone  from  Heat. — Experiments  have 
been  made  in  this  country  and  Great  Britain  to  ascertain  the 
expansion  of  stone  for  every  degree  of  Fahrenheit,  and  the 
results  have  been  tabulated.     Within  the  ordinary  ranges  of 
temperature  the  stone  is  too  slightly  affected  by  expansion  or 
contraction    to  cause    any   perceptible   change.      Professor 
Eartlett's  experiments,  however,  showed  that  in  a  long  line  of 
coping  the  expansion  was  sufficiently  great  to  crush  mortar 
between  the  blocks. 

35.  Preservation  of  Stone. — To  add  to   the  durability 
of  stone,  especially  of  that  naturally  perishable  or  showing 
signs  of  decay,  various  processes  have  been  tried  or  proposed. 
All  have  the  same  end  in  view ;  viz.,  to  fill  the  exposed 
pores  of  the  stone  with  some  substance  which  shall  exclude 
the  air  and  moisture.      Paints  and  oils  are  used  for  this  pur- 
pose.     Great  results  have  been   expected  from  the   use  of 
soluble  glass   (silicate  of  potash),  and  also  from  silicate  of 
lime.     The  former,  being  applied  in  a  state  of  solution  in 
water,  gradually  hardens,  partly  through  the  evaporation  of 
its  water,  and  partly  through  the  removal  of   the  potash  by 
the  carbonic  acid  in  the  air.     The  latter  is  used  by  filling  the 
pores  with  a  solution  of  silicate  of  potash,  and  then  introdu- 
cing a  solution  of  calcium  chloride  or  lime  nitrate ;  the  chemi- 
cal action  produces  silicate  of  lime,  filling  the  pores  of  the 
natural  stone.     Time  and  experience  will  show  if  the  hopes 
expected  from  the  use  of  these  silicates  will  be  realized. 

36.  Ease  of  Working  the  Stone. — This  property  is  to  a 
certain  extent  the  inverse  of  the  others.     The  ease  with  which 
stone  can  be  cut  or  hammered  into  shape  implies  either  soft- 
ness or  else  a  low  degree  of  cohesiveness  between  its  particles. 

It  often  happens  that  its  hardness  may  prevent  a  stone,  in 
every  other  way  suitable,  from  being  wrought  to  a  true  sur- 
face and  from  receiving  a  smooth  edge  at  the  angles.  More- 
over, the  difficulty  of  working  will  increase  very  materially 
the  cost  of  the  finished  stone. 

It  requires  experience  and  good  judgment  to  strike  a  me- 
dium between  these  conflicting  qualities. 


18  CIVIL   ENGINEERING. 

37.  Quarrying. — If  the  engineer  should  be  obliged  to  get 
out  his  own  stone  by  opening  a  new  quarry,  he  should  pay  par- 
ticular attention  to  the  best  and  cheapest  method  of  getting  it 
out  and  hauling  it  to  the  point  where  it  is  to  be  used.  In  all 
cases  he  will,  if  possible,  open  the  quarry  on  the  side  of  a 
hill,  and  arrange  the  roads  in  and  leading  to  it  with  gentle 
slopes,  so  as  to  assist  the  draught  of  the  animals  employed. 
The  stone  near  the  surface,  not  being  as  good  as  that  beneath, 
is  generally  discarded.  The  mass  or  bed  of  stone  being  ex- 
posed, a  close  inspection  will  discover  the  natural  joints  or 
fissures  along  which  the  blocks  will  easily  part  from  each 
other.  When  natural  fissures  do  not  exist,  or  smaller  blocks 
are  required,  a  line  of  holes  is  drilled  at  short  regular  inter- 
vals, or  grooves  are  cut  in  the  upper  surface  of  a  bed.  Then 
blunt  steel  wedges  or  pins,  slightly  larger  than  the  holes,  are 
inserted,  and  are  struck  sharply  and  simultaneously  with  ham- 
mers until  the  block  splits  off  from  the  layer. 

If  large  masses  of  stone  be  required,  resort  is  had  to  blast- 
ing1. This  operation  consists  in  boring  the  requisite  number 
of  holes,  loading  them  with  an  explosive  compound,  arid  fir- 
ing them.  The  success  of  blasting  will  depend  upon  a  judi- 
cious selection  of  the  position  and  depth  of  the  holes  and  upon 
the  use  of  the  proper  charges. 

Instead  of  trusting,  as  is  too  often  done,  to  an  empirical 
rule,  or  to  no  rule  at  all,  it  is  well,  by  actual  experiments  on 
the  particular  rock  to  be  quarried,  to  ascertain  the  effect  of 
different  charges,  so  as  to  determine  the  amount  required  in 
any  case,  to  produce  the  best  result. 


VARIETIES  OF  BUILDING  STONES  IN  GENERAL  USB. 
SILICIOIJS  STONES. 

38.  Silicious  Stones  are  those  in  which  silica  is  the  prin- 
cipal constituent.  With  a  few  exceptions,  their  structure  ia 
crystalline-granular,  the  grains  being  hard  and  durable.  They 
emit  sparks  when  struck  with  a  steel,  and  do  not  generally 
effervesce  with  acids. 

Some  of  the  principal  silicious  stones  used  in  building  are 
Syenite,  Granite,  Gneiss,  Mica  Slate,  Hornblende  Slate, 
Steatite,  and  the  Sandstones.  For  their  composition,  partic- 
ular description,  etc.  see  any  of  the  manuals  of  mineralogy. 

Syenite,  Granite,  and  Gneiss.— These  stones  differ  but  lit- 
tle in  the  qualities  essential  to  a  good  building  material,  and 


SILICIOC8   STONES.  19 

from  the  great  resemblance  of  their  external  characters  and 
physical  properties  are  generally  known  to  builders  by  the 
common  term  granite. 

Granite  (Syenite,  Granite,  and  Gneiss). — This  stone  ranks 
high  as  building  material,  in  consequence  of  its  superior 
strength,  hardness,  and  durability,  and  furnishes  a  material  par- 
ticularly suitable  for  structures  which  require  great  strength. 
It  does  not  resist  well  very  high  temperatures,  and  its  great 
hardness  requires  practised  stone-cutters  to  be  employed  in 
working  it  into  proper  shapes.  It  is  principally  used  in  works 
of  magnitude  and  importance,  as  light-houses,  sea-walls, 
revetment-walls  of  fortifications,  large  public  buildings,  etc. 
Only  in  districts  where  it  abounds  is  it  used  for  ordinary 
dwelling-houses.  It  was  much  used  by  the  ancients,  especially 
by  the  Egyptians,  some  of  whose  structures,  as  far  as  the  stone 
is  concerned,  are  still  remaining  in  good  condition,  after  3,000 
years'  exposure.  Granite  occurs  in  extensive  beds,  and  may 
be  obtained  from  the  quarries  in  blocks  of  almost  any  size  re- 
quired. Gneiss,  in  particular,  having  the  mica  more  in  layers, 
presents  more  of  a  stratified  appearance,  and  admits  of  being 
broken  out  into  thin  slabs  or  blocks.  A  granite  selected  for 
building  purposes  should  have  a  fine  grain,  even  texture,  and 
its  constituents  uniformly  disseminated  through  the  mass.  It 
should  be  free  from  pyrites  or  any  iron  ore,  which  will  rust 
and  deface,  if  not  destroy  the  stone  on  exposure  to  the  weath- 
er. The  feldspathic  varieties  are  the  best,  and  the  syenitic 
are  the  most  durable.  An  examination  of  the  rock  in  and 
around  the  quarry  may  give  some  idea  of  its  durability. 

Mica  Slate  bas  in  its  composition  the  same  materials  as 
gneiss,  and  breaks  with  a  glistening  or  shining  surface.  The 
compact  varieties  are  much  used  for  flagging,  for  door  and 
hearth  stones,  and  for  lining  furnaces,  as  they  can  be  broken 
out  in  thin,  even  slabs.  It  is  often  used  in  ordinary  masonry 
work,  in  districts  where  it  abounds. 

Hornblende  Slate  resembles  mica  slate,  but  is  tougher,  and 
is  an  excellent  material  for  flagging. 

Steatite,  or  Soapstone,  is  a  soft  stone  easily  cut  by  a  knife, 
and  greasy  to  the  touch.  From  the  ease  with  which-  it  is 
worked,  and  from  its  refractory  nature,  it  is  used  for  fire-stones 
in  furnaces  and  stoves,  and  for  jambs  in  fire-places.  Being 
soft,  it  is  not  suitable  for  ordinary  building  purposes. 

Sandstone  is  a  stratified  rock,  consisting  of  grains  of  silicious 
sand,  arising  from  the  disintegration  of  silicious  stones,  ce- 
mented together  by  some  material,  generally  a  compound  of 
silica,  alumina,  and  lime.  It  has  a  harsh  feel,  and  every  dull 
shade  of  color  from  white,  through  yellow,  red,  and  brown,  to 


20  CIVIL   ENGINEERING. 

nearly  a  black.  Its  strength,  hardness,  and  durability  vary 
between  very  wide  limits  ;  some  varieties  being  little  inferior 
to  good  granite  as  a  building-stone,  others  being  very  soft, 
friable,  arid  disintegrating  rapidly  when  exposed  to  the  weath- 
er. The  least  durable  sand-stones  are  those  which  contain  the 
most  argillaceous  matter ;  those  of  a  f  eldspathic  character  also 
are  found  to  withstand  poorly  the  action  of  the  weather.  The 
best  sandstone  lies  in  thick  strata,  from  which  it  can  be  cut  in 
blocks  that  show  very  faint  traces  of  stratification;  that  which 
is  easily  split  into  thin  layers,  is  weaker.  It  should  be  firm  in 
texture,  not  liable  to  peel  off  when  exposed,  and  should  be  free 
from  pyrites  or  iron-sand,  which  rust  and  disfigure  the  blocks. 
It  is  generally  porous  and  capable  of  absorbing  much  water, 
but  it  is  comparatively  little  injured  by  moisture,  unless  when 
built  with  its  layers  set  on  edge.  In  this  case  the  expansion  of 
water  between  the  layers  in  freezing  makes  them  split  or 
"  scale  "  off.  It  should  be  placed  with  the  strata  in  a  horizon- 
tal position,  so  that  any  water  which  may  penetrate  between 
the  layers  may  have  room  to  expand  or  escape.  Most  of  the 
varieties  of  sandstone  yield  readily  under  the  chisel  and  saw, 
and  split  evenly ;  from  these  properties  it  has  received  from 
workmen  the  name  of  free-stone.  It  is  used  very  exten- 
eively  as  a  building-stone,  for  flagging,  for  road  material ;  and 
Borne  of  its  varieties  furnish  an  excellent  fire-stone. 

Other  varieties  of  silicious  stones  besides  those  named,  as 
porphyry,  trap  or  greenstone,  basalt,  quartz-rock 
(cobble-stone),  buhr-stone,  etc.,  are  used  for  building  and 
engineering  purposes,  and  are  eminently  fit,  either  as  cut- 
stone  or  rubble,  as  far  as  strength  and  durability  are  concerned. 


AEGILLAOEOU8  STONES. 

39.  Argillaceous  or  Clayey  Stones  are  those  in  which 
clay  exists  in  sufficient  quantity  to  give  the  stone  its  charac- 
teristic properties.  As  a  rule,  the  natural  argillaceous  stones, 
excepting  roofing  slate,  are  deficient  in  the  properties  of  hard- 
ness and  durability,  and  are  unfit  for  use  in  engineering  con- 
structions. 

Roofing  Slate  is  a  stratified  rock  of  great  hardness  and 
density,  commonly  of  a  dark  dull  blue  or  purplish  color.  To 
be  a  good  material  for  roofing,  it  should  split  easily  into  even 
slates,  and  admit  of  being  pierced  for  nails  without  being 
fractured.  It  should  be  free  from  everything  that  can  on  ex- 
posure undergo  decomposition.  The  signs  or  good  quality  in 
slate  are  compactness,  smoothness,  uniformity  of  texture,  clear 


CALCAREOUS    STONES.  21 

dark  color;  it  should  give  a  ringing  sound  when  struck,  and 
should  absorb  but  little  water.  Being  nearly  impervious  to 
water,  it  is  principally  used  for  covering  of  roofs,  linings  oi 
water-tanks,  and  for  other  similar  purposes. 


CALCAREOUS  STONES. 


40.  Calcareous  Stones  are  those  in  which  lime  (calcium 
monoxide)  is  the  principal  constituent.     It  enters  either  as  a 
sulphate  or  carbonate. 

Calcium  Sulphate,  known  as  gypsum  in  its  natural 
state,  when  burnt  and  reduced  to  a  powder,  is  known  as 
plaster-of-Paris.  A  paste  made  of  this  powder  and  a  little 
water,  soon  becomes  hard  and  compact.  Gypsum  is  not 
used  as  a  building-stone,  being  too  soft.  The  plaster,  owing 
to  its  snowy  whiteness  and  fine  texture,  is  used  for  taking  casts, 
making  models,  and  for  giving  a  hard  finish  to  walls.  Care 
must  be  taken  to  use  it  only  in  dry  and  protected  situations, 
as  it  absorbs  moisture  freely,  then  swells,  cracks,  and  exfoliates 
rapidly. 

Calcium  Carbonates,  or  Limestones,  furnish  a  large 
amount  of  ordinary  building-stone,  ornamental  stone,  and  form 
the  source  of  the  principal  ingredient  of  cements  and  mortars. 

They  are  distinguished  by  being  easily  scratched  with  a 
knife,  and  by  effervescing  with  an  acid.  In  texture  they  are 
either  compact  or  granular;  in  the  former  case  the  fracture  is 
smooth,  often  conchoidal ;  in  the  latter  it  has  a  crystalline- 
granular  surface,  the  fine  varieties  resembling  loaf-sugar. 

The  limestones  are  generally  impure  carbonates,  and  we 
are  indebted  to  their  impurities  for  some  of  the  most  beauti- 
ful as  well  as  the  most  invaluable  materials  used  for  construc- 
tions. Those  stones  which  are  colored  by  metallic  oxides,  or 
by  the  presence  of  other  minerals,  furnish  the  numerous  color- 
ed and  variegated  marbles  ;  while  those  which  contain  a  cer- 
tain proportion  of  impurities  as  silica,  alumina,  etc.,  yield,  on 
calcination,  those  cements  which,  from  possessing  the  prop- 
erty of  hardening  under  water,  have  received  the  names  of 
hydraulic  lime,  hydraulic  cement,  etc. 

Limestones  that  can  be  made  to  have  a  smooth  surface  and 
take  a  polish  are  known  as  marbles  ;  the  coarser  kinds 
are  called  common  limestones,  and  form  a  large  class  of 
much  value  for  building  purposes. 

41.  Marbles. — Owing  to  the  high  polish  of  which  they 
are  susceptible,  and  their  consequent  value,  the  marbles  are 
mostly  reserved  for  ornamental  purposes. 


22  CIVIL   ENGINEERING. 

They  present  great  variety,  both  in  color  and  appearance, 
and  the  different  kinds  have  generally  received  some  appro- 
priate name  descriptive  of  their  use  or  appearance. 

Statuary  Marble  is  of  the  purest  white,  finest  grain,  and 
is  free  from  all  foreign  minerals.  It  receives  a  delicate 
polish,  without  glare,  and  is,  therefore,  admirably  adapted  to 
the  purposes  of  the  sculptor,  for  whose  uses  it  is  mostly 
reserved. 

Conglomerate  Marble. — This  consists  of  two  varieties; 
the  one  termed  pudding  stone,  composed  of  rounded  pebbles 
embedded  in  compact  limestone ;  the  other  termed  breccia, 
consisting  of  angular  fragments  united  in  a  similar  manner. 
The  colors  of  these  marbles  are  generally  variegated,  making 
the  material  very  handsome  and  ornamental. 

Bird's-eye  Marble. — The  name  of  this  stone  is  descriptive 
of  its  appearance  after  sawing  or  splitting,  the  eyes  arising 
from  the  cross-sections  of  a  peculiar  fossil  (jucoides  demissus) 
contained  in  the  mass. 

Lumachella  Marble. — This  is  a  limestone  having  shells 
embedded  in  it,  and  takes  its  name  from  this  circumstance. 

Verd  Antique. — This  is  a  rare  and  costly  variety,  of 
a  beautiful  green  color,  the  latter  being  caused  by  veins 
and  blotches  of  serpentine  diffused  through  the  lime- 
stone. 

There  are  many  other  varieties  that  receive  their  name 
either  from  their  appearance  or  the  localities  from  which 
they  are  obtained. 

Many  of  these  are  imitated  by  dealers,  who,  by  processes 
known  to  themselves,  stain  the  common  marbles  so  success- 
fully that  it  requires  a  close  examination  to  distinguish  the 
false  from  the  real. 

Common  Limestone. 

42.  This  class  furnishes  a  great  variety  of  building-stones, 
which  present  great  diversity  in  their  physical  properties. 
Some  of  them  seem  as  durable  as  the  best  silicious  stones,  and 
are  but  little  inferior  to  them  in  strength  and  hardness ;  others 
decompose  rapidly  on  exposure  to  the  weather  ;  and  some 
kinds  are  so  soft  that,  when  first  quarried,  they  can  be 
scratched  with  the  nail  and  broken  between  the  fingers.  The 
durability  of  limestones  is  materially  affected  by  the  foreign 
minerals  they  may  contain  ;  the  presence  of  clay  injures  the 
stone  for  building  purposes,  particularly  when,  as  sometimes 
happens,  it  runs  through  the  bed  in  very  minute  veins 
blocks  of  stone  having  this  imperfection  soon  separate 


BRICK.  23 

these  veins  on  exposure  to  moisture.  Ferrous  oxide,  sulphate 
and  carbonate  of  iron,  when  present,  are  also  very  destructive 
in  their  effects,  frequently  causing  by  their  chemical  changes 
rapid  disintegration. 

Among  the  varieties  of  impure  carbonates  of  lime  are  the 
magnesian  limestones,  called  dolomites.  They  are  re- 
garded in  Europe  as  a  superior  building  material ;  those  being 
considered  the  best  which  are  most  crystalline,  and  are  com- 
posed of  nearly  equal  proportions  of  the  carbonates  of  lime 
and  magnesia.  The  magnesian  limestone  obtained  from 
quarries  in  New  York  and  Massachusetts  is  not  of  such  good 
quality ;  the  stone  obtained  being,  in  some  cases,  extremely 
friable. 


EL— ARTIFICIAL  STONES. 
1st — BRICK. 

43.  A  brick  is  an  artificial  stone,  made  by  moulding  tem- 
pered clay  into  a  form  of  the  requisite  shape  and  size,  and 
hardening  it,  either  by  baking  in  the  sun  or  by  burning  in  a 
kiln  or  other  contrivance,     when  hardened  by  the  h'rst  pro- 
cess, they  are  known  as  sun-dried,  and  by  the  latter  as  burnt- 
brick,  or  simply  brick. 

44.  Sun  dried  Brick. — Sun-dried  bricks  have  been  in  use 
from  the  remotest  antiquity,  having  been  found  in  the  ruins 
of  ancient  Babylon.     They  were  used  by  the  Greeks  and 
Romans,  and  especially  by  the  Egyptians.     At  present  they 
are  seldom  employed. 

They  were  ordinarily  made  in  the  spring  or  autumn,  as 
they  dried  more  uniformly  during  those  seasons ;  those  made 
in  the  summer,  drying  too  rapidly  on  the  exterior,  were  apt 
to  crack  from  subsequent  contraction  in  the  interior. 

It  was  not  customary  to  use  them  until  two  years  after  they 
had  been  made. 

"Walls,  known  as  adobes,  made  of  earth  hardened  in  a  simi- 
lar way,  are  found  in  parts  of  our  country  and  in  Mexico. 
They  furnish  a  simple  and  economical  mode  of  construction 
where  the  weights  to  be  supported  are  moderate,  and  where 
fuel  is  very  scarce  and  expensive.  This  mode,  however  suit- 
able for  a  southern,  is  not  fit  for  our  climate. 

45.  Burnt  Brick. — Bricks    may    be    either    common  T>r 
pressed,  hand  or  machine  made. 

The  qualities  of  a  brick  are  dependent  upon  the  kind  of 


24  CIVIL   ENGINEERING. 

earth  used,  the  tempering  of  this  earth,  the  moulding  of  the 
raw  brick,  and  the  drying  and  burning  processes. 

46.  Common  Brick.— The  size  and  form  of  common  bricks 
vary  "but  little.  They  are  generally  rectangular  parallelopi- 
pedons,  about  8£  inches  long,  4  inches  broad,  and  2f  inches 
thick,  the  exact  size  varying  with  the  contraction  of  the  clay. 

Kinds  of  Earth. — The  argillaceous  earths  suitable  for 
brick-making  may  be  divided  into  three  principal  classes,  viz. : 

Pure  Clays,  those  composed  chiefly  of  aluminum  silicate, 
or  one  part  of  alumina  and  two  of  silica,  combined  with  a 
small  proportion  of  other  substances,  as  lime,  soda,  magnesia, 
ferrous  oxide,  etc.; 

Loams,  which  are  mechanical  mixtures  of  clay  and  sand ; 
and 

Marls,  which  are  mechanical  mixtures  of  clay  and  car- 
bonate of  lime. 

Pure  clay,  being  made  plastic  with  water,  may  be  moulded 
into  any  shape,  but  will  shrink  and  crack  in  drying,  however 
carefully  and  slowly  the  operation  be  conducted.  By  mixing 
a  given  quantity  of  sand  with  it,  these  defects  may  be  greatly 
remedied,  while  the  plastic  quality  of  the  clay  will  not  be 
materially  affected. 

The  loams  oftentimes  have  too  much  sand,  and  are  then  so 
loose  as  to  require  an  addition  of  clay  or  other  plastic  mate- 
rial to  increase  their  tenacity. 

Earth  is  frequently  found  containing  the  proper  proportions 
of  clay  and  sand  suitable  for  making  bricks ;  but,  if  it  be  not 
naturally  fit  for  the  purpose,  it  should  be  made  so  by  adding 
that  element  which  is  lacking.  The  proportion  of  sand  or 
clay  to  be  added  should  be  determined  by  direct  experiments. 

Silicate  of  lime,  if  in  any  considerable  quantity  in.  the 
earth,  makes  it  too  fusible.  Carbonate  of  lime,  if  present 
in  any  considerable  quantity  in  the  earth,  would  render  it 
unfit,  ^since  the  carbonate  is  converted,  during  the  burning, 
into  lime,  which  absorbs  moisture  upon  being  exposed,  would 
cause  disintegration  in  the  brick. 

Preparation  of  the  Earth. — The  earth,  being  of  the  proper 
kind,  is  first  dug  out  before  the  cold  weather,  and  carried 
to  a  place  prepared  to  receive  it.  It  is  there  piled  into  heaps 
and  exposed  to  the  weather  during  the  winter,  so  as  to  be 
mellowed  by  the  frosts,  which  break  up  and  crumble  the 
lumps. 

In  the  spring  the  earth  is  turned  over  with  shovels,  and  the 
stones,  pebbles,  and  gravel  are  removed  ;  if  either  clay  or 
sand  be  wanting,  the  proper  amount  is  added. 

Tempering — The  object  of  tempering  is  to  bring  the  earth 


BRICK.  25 

into  a  homogeneous  paste  for  the  use  of  the  moulder.  This 
is  effected  by  mixing  it  with  about  half  its  volume  of  water, 
and  stirring  it  and  kneading  it  either  *by  turning  it  over  re- 
peatedly with  shovels  and  treading  it  over  by  horses  or  men 
until  the  required  plasticity  is  obtained,  or  by  using  the  pug- 
mill  or  a  similar  machine. 

The  plastic  mass  is  then  moulded  into  the  proper  forms  by 
hand  or  machinery. 

By  Hand. — In  the  process  by  hand  the  mould  used  is  a 
kind  of  box,  without  top  or  bottom,  and  the  tempered  clay  is 
dashed  into  it  with  sufficient  force  to  complete!}7  fill  it,  the 
superfluous  clay  being  removed  by  striking  it  with  a  straight- 
edge. The  newly-made  brick  is  then  turned  out  on  a  drying- 
floor,  or  on  a  board  and  carried  to  the  place  where  it  is  to 
dry. 

47.  By  Machines. — Bricks  are  now  generally  moulded  by 
machines.     These  machines  combine  the  pug-mill  with  an 
apparatus  for  moulding.     This  apparatus  receives  the  clay  as 
discharged  from  the  pug-mill,  presses  it  in  moulds,  and  pushes 
the  brick  out  in  front  ready  to  be  removed  from  the  frames 
and  carried  to  the  drying-floor. 

48.  Drying. — Great  attention  is  necessary  in  this  part  of 
the  process  of  manufacture.     The  raw  bricks  are  dried  in  the 
open  air  or  in  a  drying-house,  where  they  are  spread  out  on 
the  ground  or  floor,  and  are  frequently  turned  over  until  they 
are  sufliciently  hard  to  be  handled  without  injury.     They  are 
then  piled  into  stacks  under  cover  for  further  drying. 

In  drying  bricks,  the  main  points  to  be  observed  are  to  pro- 
tect them  from  the  direct  action  of  the  sun,  from  draughts  of 
air,  from  rain  and  frost,  and  to  have  each  brick  dry  uni- 
formly from  the  exterior  inwards.  The  time  allowed  for  dry- 
ing depends  upon  the  climate,  the  season  of  the  year,  and  the 
weather. 

49.  Burning-. — The  next  stage  of  manufacture  is  the  burn- 
ing.    The  bricks  are  arranged  in  the  kiln  so  as  to  allow  the 
passage  of  the  heat  around  them ;  this  is  effected  by  piling 
the  bricks  so  that  a  space  is  left  around  each.     This  arrange- 
ment of  the  bricks,  called  setting  the  kiln,  is  to  allow  the  heat 
to  be  diffused  equally  throughout,  to  afford  a  good  draught, 
and  to  keep  up  a  steady  heat  with  the  least  amount  of  fuel. 

A  very  moderate  fire  is  next  applied  under  the  arches  of 
the  kiln  to  expel  any  remaining  moisture  from  the  raw  brick ; 
this  is  continued  until  the  smoke  from  the  kiln  is  no  longer 
black.  The  fire  is  then  increased  until  the  bricks  of  the 
arches  attain  a  white  heat ;  it  is  then  allowed  to  abate  in  some 
degree,  in  order  to  prevent  complete  vitrif action ;  and  it  is 


26  CIVIL   ENGINEERING. 

thus  alternately  raised  and  lowered  until  the  burning  is  com- 
plete, as  ascertained  by  examining  the  bricks  at  the  top  of  the 
kiln.'  The  bricks  should  be  slowly  cooled;  otherwise  they 
will  not  withstand  the  effects  of  the  weather.  The  cooling  is 
done  by  closing  the  mouths  of  the  arches  and  the  top  and 
sides  of  the  kiln,  in  the  most  effectual  manner,  with  moist  clay 
and  burnt  brick,  and  by  allowing  the  kiln  to  remain  in  this 
state  until  the  heat  has  subsided.  The  length  of  time  of  burn- 
ing varies,  but  is  often  fifteen  days  or  thereabouts. 

50.  General  Qualities  and  Uses. — Bricks,  when  properly 
burnt,  acquire  a  degree  of  hardness  and  durability  that  ren- 
ders them  suitable  for  nearly  all  the  purposes  to  which  stone 
is  applicable  ;  for,  when  carefully  made,  they  are  in  strength, 
hardness,  and  durability  but  little  inferior  to  the  ordinary 
kinds  of  building-stone.     They  remain  unchanged  under  the 
extremes  of  temperature,  resist  the  action  of  water,  set  firmly 
and  promptly  with  mortar,  and,  being   both  cheaper   and 
lighter  than  stone,  are  preferable  to  it  for  many  kinds  of 
structures,  as  for  the  walls  of  houses,  small  arches,  etc. 

The  Romans  employed  bricks  in  the  greater  part  of  their 
constructions.  The  scarcity  of  stone  in  Holland  and  the 
Netherlands  led  to  their  extensive  use,  not  only  in  private 
but  in  their  public  buildings,  and  these  countries  abound 
in  fine  specimens  of  brick-work. 

51.  Characteristics  of  good  Bricks. — Good  bricks  should 
be  regular  in  shape,  with  plane  surfaces  and  sharp  edges; 
the  opposite  faces  should  be  parallel,  and  adjacent  faces  per- 
pendicular to  each  other. 

They  should  be  free  from  cracks  and  flaws ;  be  hard ; 
possess  a  regular  form,  and  uniform  size ;  and,  where  exposed 
to  great  heat,  infusibility. 

They  should  give  a  clear,  ringing  sound  when  struck ;  and 
when  broken  across,  they  should  show  a  fine,  compact,  uni- 
form texture,  free  from  air-bubbles  and  cracks. 

They  should  not  absorb  more  than  J-g-  of  their  weight  of  water. 

52.  From  the  nature  of  the  process  of  burning,  it  will  be 
evident  that  in  the  same  kiln  must  be  found  bricks  of  very 
different  qualities.     There  will  be  at  least  three  varieties:  1, 
bricks  which  are  burned  too  much  ;  2,  those,  just  enough  ;  and, 
3,  those,  not  enough.     The  bricks  forming  the  arches  and  ad- 
jacent to  the  latter,  being  nearer  the  fire,  will  be  burnt  to 
great  hardness,  or  perhaps  vitrified  ;  those  in  the  interior  will 
be  well  burnt ;  and  those  on  top  and  near  the  exterior  will 
be  under-burned.     The  first  are  called  arch  brick  ;   the  sec- 
ond, body,  hard,  or,  if  the  clay  had  contained  ferrous-oxide, 
cherry  red  j  and  the  third,  soft,  pale,  or  sammel  brick. 


TILES.  27 

The  arch  bricks  are  very  hard  but  brittle,  and  have  but 
slight  adhesion  with  mortar ;  the'  soft  or  sammel,  if  exposed 
to  the  weather,  have  not  requisite  strength  or  durability, 
and  can,  therefore,  be  used  only  for  inside  work. 

53.  Pressed  Brick. — Pressed  brick  are  made  by  putting 
the  raw  bricks,  when  nearly  dry,  into  moulds  of  proper 
shape,  and  submitting  them  to  a  heavy  pressure  by  machinery. 
They  are  heavier  than  the  common  brick.  All  machine- 
made  bricks  partake  somewhat  of  the  nature  of  pressed 
brick. 

54  Fire-bricks. — Fire-bricks  are  made  of  refractory  clay 
which  contains  no  lime  or  alkaline  matter,  and  remains  un- 
changed by  a  degree  of  heat  that  would  vitrify  and  destroy 
common  brick.  They  are  ~baked  rather  than  burnt,  and  their 
quality  depends  upon  the  fineness  to  which  the  clay  has  been 
ground  and  the  degree  of  heat  used  in  making  them. 

They  are  used  for  facing  fireplaces,  lining  furnaces,  and 
wherever  a  high  degree  of  temperature  is  to  be  sustained. 

Bricks  light  enough  to  float  in  water  were  known  to  the 
ancients.  During  the  latter  part  of  the  last  century  M.  Fab- 
broni,  of  Italy,  succeeded  in  making  floating  bricks  of  a  ma- 
terial known  as  agaric  mineral,  a  kind  of  calcareous  tufa, 
called  fossil  meal.  Their  weight  was  only  one-sixth  that  of 
common  brick ;  they  were  not  affected  by  the  highest  tem- 
perature, and  were  bad  conductors  of  heat. 

55.  Brick-making  was  introduced   into  England  by  the 
Romans,  and  arrived  at  great  perfection  during  the  reign  of 
Henry  YIII. 

The  art  of  brick-making  is  now  a  distinct  branch  of  the 
useful  arts,  and  the  number  of  bricks  annually  made  in  this 
country  is  very  great,  amounting  to  thousands  of  millions. 

The  art  of  brick-making  does  not  belong  to  that  of  the  en- 
gineer. But  as  the  engineer  may,  under  peculiar  circum- 
stances, be  obliged  to  manufacture  brick,  the  foregoing  out- 
line has  been  given. 

Tiles. 

56.  Tiles  are  a  variety  of  brick,  and  from  their  various 
uses  are  divided  into  three  classes,  viz. :  roofing1,  paving,  and 
draining  tiles. 

Their  manufacture  is  very  similar  to  that  of  brick,  the 
principal  differences  arising  from  their  thinness.  This  re- 
quires the  clay  to  be  stronger  and  purer,  and  greater  care  tc 
be  taken  in  their  manufacture. 

Their  names  explain  their  use. 


CIVIL  ENGINEERING. 


2d. CONCRETES. 

57.  Concrete  is  the  term  applied  to  any  mixture  of  incrta* 
with  coarse  solid  materials,  as  gravel,  pebbles,  shells,  or  frag- 
ments of  brick,  tile,  or  stone. 

The  term  concrete  was  formerly  applied  to  the  mixture 
made  with  common  lime  mortar ;  beton,  to  the  mixture  when 
the  mortar  used  was  hydraulic,  i.  e.,  will  harden  under  water. 

The  proportions  of  mortar  and  coarse  materials  are  de- 
termined by  the  following  principle:  that  the  volume  of 
cementing  substance  should  always  ~be  slightly  in  excess  of  the 
volume  of  voids  of  the  coarse  materials  to  be  united.  This 
excess  is  added  as  a  precaution  against  imperfect  manipula- 
tion. 

Concrete  is  mixed  by  hand  or  by  machinery. 

One  method,  by  hand,  used  at  Fort  Warren,  Boston  Harbor, 
was  as  follows :  The  concrete  was  prepared  by  lirst  spread- 
ing out  the  gravel  on  a  platform  of  rough  boards,  in  a  layer 
from  eight  to  twelve  inches  thick,  the  smaller  pebbles  at  the 
bottom  and  the  larger  on  the  top,  and  then  spreading  the 
mortar  over  it  as  uniformly  as  possible.  The  materials  were 
then  mixed  by  four  men,  two  with  shovels  and  two  with  hoes, 
the  former  facing  each  other,  always  working  from  the  out- 
side of  the  heap  to  the  centre,  then  stepping  back,  and  recom- 
mencing in  the  same  way,  and  continuing  the  operation  until 
the  whole  mass  was  turned.  The  men  with  hoes  worked  each 
in  conjunction  with  a  shoveller,  and  were  required  to  rub  well 
into  trie  mortar  each  shovelful  as  it  was  turned  and  spread. 
The  heap  was  turned  over  a  second  time,  this  having  been 
usually  sufficient  to  make  the  mixture  complete,  to  cover  the 
entire  surface  of  each  pebble  with  mortar,  and  to  leave  the 
mass  of  concrete  ready  for  use. 

Yarious  machines  have  been  devised  to  effect  the  thorough 
mixing  of  the  materials.  A  pug-mill,  a  cylinder  in  an  in- 
clined position  revolving  around  its  axis,  a  cubical  box  revolv- 
ing eccentrically,  and  various  other  machines,  have  been  used. 

58.  Uses  of  Concrete. — Concrete  has  been  generally  used 
in  confined  situations,  as  foundations,  or  as  a  backing  for  mas- 
sive walls.     For  many  years  it  has  been  extensively  employed 
in  the  construction  of  the  public  works  throughout  the  U  nited 
States,  and  is  now  extended  in  its  application,  not  only  to 
foundations,  but  even  to  the  building  of  exterior  and  partition 
walls  in  private  buildings.     It  has  of  recent  years  had  quite 
an  extensive  application  in  harbor  improvements  in  Europe. 
There  are  evidences  of   its  extensive  use  in  ancient  times 


PATENT   STONES.  2P 

in  Rome ;  many  public  buildings,  palaces,  theatres,  aqueducts, 
etc.,  being  built  of  this  material.  It  has  been  asserted  that 
the  pyramids  of  Egypt  are  built  of  artificial  stone  composed 
of  small  stone  and  mortar. 

It  is  especially  suitable  as  a  building  material  when  dry  ness, 
water-tightness,  and  security  against  vermin  are  of  conse- 
quence, as  in  cellars  of  dwelling-houses,  magazines  on  the 
ground,  or  underneath, for  storage  of  provisions,  etc. 

59.  Remarks. — In  order  to  obtain  uniformly  a  good  con- 
crete by  the  use  of  hydraulic  lime  or  cement,  or  both,  it  is 
essential — 

1.  That  the  amount  of  water  be  just  sufficient  to  form  the 
cementing  material  into  a  viscous  paste,  and  that  it  be  sys- 
tematically applied ; 

2.  That  each  grain  of  sand  or  gravel  be  entirely  covered 
with  a  thin  coating  of  this  paste ;  and 

3.  That  the  grains  be  brought  into  close  and  intimate  con- 
tact with  each  other. 

These  conditions  require  more  than  the  ordinary  methods 
and  machinery  used  in  making  mortars,  especially  if  a  supe- 
rior article  be  desired. 


Patent  Stones. 

60.  Various  attempts  from  time  to  time  have  been  made  to 
make  an  imitation  which,  possessing  all  the  merits,  and  being 
free  from  the  defects,  of  the  most  useful  building-stones, 
would  supplement,  if  not  supersede,  them.  These  imitations 
are  generally  artificial  sandstones. 


Beton  Agglomere. 

61.  Beton  agglomere,  or  Coignet-Beton,  is  an  arti- 
ficial sandstone,  made  by  M.  Francois  Coignet,  of  Paris, 
France,  in  which  the  grains  of  sand  are  cemented  together 
by  a  lime  paste  possessing  hydraulic  properties. 

It  is  made  by  placing  the  hydraulic  cement  with  about 
one-third  its  volume  of  water  into  a  mill,  and  mixing  until 
a  plastic  and  sticky  paste  is  formed.  This  paste  and  per- 
fectly dry  sand,  in  suitable  proportions,  are  then  put  into  a 
powerful  mill  and  mixed  together  until  a  pasty  powder  is 
formed.  The  pasty  powder  is  placed  in  layers  of  from 
one  and  a  half  to  two  inches  thick,  in  strong  moulds,  and 
rammed  by  repeated  blows  of  an  iron-shod  rammer  until  each 


30  CIVIL   ENGINEERING. 

layer  of  material  is  reduced  to  about  one-third  of  its  origi- 
nal  thickness.  The  upper  surface  is  struck  with  a  straight- 
edge, and  smoothed  off  with  a  trowel.  The  mould  is  turned 
over  on  a  bed  of  sand,  and  detached  from  the  block.  If  the 
block  be  small,  it  may  be  handled  after  one  day;  larger 
pieces  should  have  a  longer  time  to  harden. 

In  common  practice,  the  cement  and  the  sand  in  a  dry 
state  are  mixed  with  shovels,  spread  out  on  the  floor,  and 
then  sprinkled  with  the  proper  amount  of  water.  The  damp- 
ened mixture  is  shovelled  into  the  mill  and  thoroughly 
mixed. 

The  proportions  of  sand  and  lime  will  vary  according  to 
the  probable  uses  of  the  stone ;  6  volumes  of  sand  to  1  of 
hydraulic  lime  in  powder ;  or,  5  of  sand,  1  of  hydraulic  lime, 
and  1  of  Portland  cement,  are  sometimes  used. 

The  distinctive  features  of  this  beton  are  the  very  small 
proportion  of  water  used,  the  thorough  mixing  of  the  materi- 
als, and  the  consolidation  effected  by  ramming  the  layers. 

If  too  much  water  be  used,  the  mixture  cannot  be  suitably 
rammed  ;  if  too  little,  it  will  be  deficient  in  strength. 

Beton  agglomere  is  noted  for  its  strength,  hardness,  and 
durability,  and  has  had  quite  an  extensive  application  in 
France ;  'aqueducts,  bridges,  sewers,  cellars  of  barracks,  etc., 
have  been  built  with  it. 


Ransome's  Patent  Stone. 

62.  Among  other  artificial  stones  that  are  offered  to  the 
builder  are  several  bearing  the  name  of  Kansome,  an  English 
engineer.  The  patent  silicious  stone,  Ransome's  apoenite,  and 
Ransome's  patent  stone,  are  all  artificial  sandstones,  in  which 
the  cement  is  a  silicate  of  lime.  They  differ  mostly  in  the 
process  of  making. 

A  patent  stone  has  been  made  in  San  Francisco  and  in 
Chicago,  and  employed  to  some  extent  in  those  cities. 

Principles  of  Manufacture. — Dry  sand  and  a  solution  of 
silicate  of  soda,  about  a  gallon  of  the  silicate  to  a  bushel  of 
sand,  are  thoroughly  mixed  in  a  suitable  mill,  and  then 
moulded  into  any  of  the  forms  required.  These  blocks  or 
forms  are  then  saturated  by  a  concentrated  solution  of  calcium 
chloride,  which  is  forced  through  the  moulded  mass  by  exhaus- 
tion of  the  air,  by  gravity,  or  by  other  suitable  means.  The 
chemical  reactions  result  in  the  formation  of  an  insoluble 


ASPHALTIO   CONCRETE.  31 

Bilicate  of  lirne,  which  firmly  unites  all  the  grains  of  the  mass 
into  one  solid,  and  a  solution  of  sodium  chloride  (common 
salt).  The  latter  is  removed  by  washing  with  water. 

Remark. — The  artificial  stone  thus  formed  is  uniform  and 
homogeneous  in  its  texture,  and  said  to  be  free  from  liability 
to  distortion  or  shrinkage.  It  is  also  claimed  that  it  is  not 
affected  by  variations  of  climate  or  temperature. 


3D. ASPHALTIO   CONCRETE. 

63.  Asphaltic  Concrete  is  a  concrete  in  which  the  solid 
materials  are  united  by  mastic,  a  mixture  of  powdered  lime- 
stone, or  similar  material,  with  artificial  or  natural  combina- 
tions of  bituminous  or  resinous  substances. 

The  manufacture  of  mastics  will  be  described  under  the 
head  of  UNITING  MATERIALS  ;  the  manufactured  product  may 
be  bought  in  blocks  ready  for  use. 

Asphaltic  concrete  is  made  as  follows : 

The  mastic  is  broken  into  small  pieces,  not  more  than  half 
a  pound  each,  and  placed  in  a  caldron,  or  iron  pot,  over  a  fire. 
It  is  constantly  stirred  to  prevent  its  burning,  and  as  soon  as 
melted  there  is  gradually  added  two  parts  of  sand  to  each 
one  of  the  mastic,  and  the  whole  mass  is  constantly  stirred 
until  the  mixture  will  drop  freely  from  the  implement  used 
in  stirring. 

The  ground  having  been  made  perfectly  firm  and  smooth, 
covered  with  ordinary  concrete,  or  otherwise  prepared,  the 
mixture  is  applied  by  pouring  it  on  the  surface  to  be  coated, 
taking  care  to  spread  it  uniformly  and  evenly  throughout. 
A  square  or  rectangular  strip  is  first  laid,  and  then  a  second, 
and  so  on,  until  the  entire  surface  is  completely  covered,  the 
surface  of  each  square  being  smoothed  with  the  float.  Before 
the  concrete  hardens  a  small  quantity  of  fine  sand  is  sifted 
over  it  and  is  well  rubbed  in  with  a  trowel  or  hand-float. 

The  thickness  of  the  coating  will  depend  upon  its  situa- 
tion, being  less  for  the  capping  of  an  arch  than  for  the  floor- 
ing of  a  room,  and  less  for  the  latter  than  for  a  hall  or  pave- 
ment that  is  to  be  in  constant  use. 

Care  is  taken  to  form  a  perfect  union  between  edges  of 
adjoining  squares,  and,  where  two  or  more  thicknesses  are 
used,  to  make  them  break  joints. 

A  mixture  of  coal  tar  is  frequently  used  as  a  substitute  for 
mastic. 

Uses. — The  principal  uses  of  asphaltic  concrete  are  for  pav 
ing  streets,  side- walks,  floors  of  cellars,  etc. 


32  CIVIL  ENGINEERING. 


4TH. GLASS. 

64.  Glass  is  a  mixture  of  various  insoluble  silicates.     Its 
manufacture  depends  upon  the  property  belonging  to  the  al- 
kaline silicates,  when  in  a  state  of  fusion,  of  dissolving  a 
large  quantity  of  silica.     The  mixture  hardens  on  cooling, 
and  is  destitute  of  crystalline  structure. 

Uses. — Glass  is  extensively  used  in  building,  as  a  roof- 
covering  for  conservatories,  ornamental  buildings,  railroad 
depots,  and  other  structures  for  which  the  greatest  possible 
light  or  the  best-looking  material  is  required.  Other  uses, 
as  for  windows,  sky-lights,  doors,  etc.,  are  familiar  to  every 
one. 

65.  Glazing  is  the  art  of  fixing  glass  in  the  frames  of  win- 
dows.    The  panes  are  secured  with  putty,  a  composition  of 
whiting  and  linseed-oil  with  sometimes  an  addition  of  white 
lead.     Large  panes  should  be  additionally  secured  by  means 
of  small  nails  or  brads. 


CHAPTER  III. 
METALS. 

66.  The  metals  used  in  engineering  constructions  are  Iron, 
Steel,  Copper,  Zinc,  Tin,  Lead,  and  some  of  their  alloys. 

IRON  AND  STEEL. 

67.  Iron  has  the  most  extensive  application  of  all  the 
metals  used  for  building  purposes.     It  is  obtained  from  tho 
ore  by  smelting  the  latter  in  a  blast-furnace.     When  the  fuel 
used  is  coal,  the  blast  is  generally  of  hot-air;  in  this  process, 
known  as  the  hot-blast*  the  air,  before  being  forced  into  the 
furnace,  is  heated  high  enough  to  melt  lead. 

When  the  metal  has  fused,  it  is  separated  from  the  other 
substances  in  the  ore,  and  is  allowed  to  combine  with  a  small 
amount  of  carbon,  from  2  to  5  per  cent.,  forming  a  com- 
pound known  as  cast-iron. 

A  sufficiency  of  cast-iron  having  accumulated  in  the  fur- 


CAST-IBON.  33 

aace,  the  latter  is  tapped,  and  the  molten  metal  running  out 
is  received  in  sand  in  long  straight  gutters,  which  have 
numerous  side  branches.  This  arrangement  is  called  the  sow 
and  pigs  ;  hence  the  name  of  pig-iron. 

The  iron  in  the  pig  is  in  a  shape  to  be  sent  to  market,  and 
in  suitable  condition  to  be  remelted  and  cast  into  any  re- 
quired form,  or  to  be  converted  into  wrought  or  malleable 
iron. 

Impurities. — The  strength  and  other  good  equalities  of  the 
iron  depend  mainly  on  the  absence  of  impurities,  and  espe- 
cially of  those  substances  known  to  cause  brittleness  and  weak- 
ness, as  sulphur,  phosphorus,  silicon,  calcium,  and  magnesium. 


CAST-IRON-. 

68.  Cast-iron  is  a  valuable  building  material,  on  account 
of  its  great  strength,  hardness,  and  durability,  and  the  ease 
with  which  it  can  be  cast  or  moulded  into  the  best  forms  for 
the  purposes  to  which  it  is  to  be  applied 

Varieties  of  Cast-iron.— Cast-iron  is  divided  into  six  varie- 
ties, according  to  their  relative  hardness.  This  hardness 
seems  to  depend  upon  the  proportion  and  state  of  carbon  in 
the  metal,  and  apparently  not  so  much  on  the  total  amount 
of  carbon  present  in  the  specimen,  as  on  the  proportionate 
amounts  in  the  respective  states  of  mechanical  mixture  and 
of  chemical  combination.  Manufacturers  distinguish  tho 
different  varieties  by  the  consecutive  whole  numbers  from  1 
to  6. 

No.  1  is  known  as  gray  cast-iron,  and  No.  6  as  white 
cast-iron.  They  are  the  two  principal  varieties. 

Gray  Cast-iron,  of  good  quality,  is  slightly  malleable  when 
cold,  and  will  yield  readily  to  the  action  of  the  file  if  the 
hard  outside  coating  is  removed.  It  has  a  brilliant  fracture  of 
a  gray,  sometimes  bluish  gray,  color.  It  is  softer  and  tough- 
er, and  melts  at  a  lower  temperature,  than  white  iron. 

White  Cast-Iron  is  very  brittle,  resists  the  file  and  chisel, 
and  is  susceptible  of  high  polish.  Its  fracture  presents  a  sil- 
very appearance,  generally  fine-grained  and  compact. 

The  intermediate  varieties,  as  they  approach  in  appear- 
ance to  that  of  No.  1  or  No.  6,  partake  more  or  less  of  the 
properties  characteristic  of  the  extreme  varieties. 

iN  umbers  2  and  3,  as  they  are  designated,  are  usually  con- 
sidered the  best  for  building  purposes,  as  combining  strength 
and  pliability. 

3 


34  CIVIL   ENGINEERING. 


Appearances  of  Good  Cast-iron. 

69.  A  medium-sized  grain  with  a  close  compact  texture  in 
dicates  a  good  quality  of  iron.     The  color  and  lustre  present- 
ed by  the  surface  of  a  recent  fracture  are  good  indications  of 
its  quality.     A  uniform  dark-gray'color  with  a  high  metallic 
lustre  is  an  indication  of  the  best  and  strongest  iron.     With 
the  same  color,  but  less  lustre,  the  iron  will  be  found  to  be 
softer  and  weaker.     No  lustre  with  a  dark  and  mottled  color 
indicates  the  softest  and  weakest  of  the  gray  varieties. 

Cast-iron,  of  a  light-gray  color  and  high  metallic  lustre,  is 
usually  very  hard  and  tenacious.  As  the  color  approaches  to 
white,  and  as  the  metallic  changes  to  a  vitreous  lustre,  hard- 
ness and  brittleness  of  the  iron  become  more  marked  ;  when 
the  extreme,  a  dull  or  grayish  white  color  with  a  very  high 
vitreous  lustre,  is  attained,  the  iron  is  of  the  hardest  and  most 
brittle  of  the  white  variety. 

70.  Test  of  its  Quality. — The  quality  of  cast-iron  may  be 
tested  by  striking  a  smart  stroke  with  a  hammer  on  the  edge 
of   a  casting.     If  the  blow  produces  a  slight  indentation, 
without  any  appearance  of  fracture,  the  iron  is  shown  to  be 
slightly  malleable,  and  therefore  of  a  good  quality ;  if,  on 
the  contrary,  the  edge  is  broken,  there  is  an  indication  of  brit- 
tleness in  the  material,  and  consequent  want  of  strength. 

71.  Strength. — The  strength  of  cast-iron  varies  with  its 
density,  and  the  density  depends  upon  the  temperature  of  the 
metal  when  drawn  from  the  furnace,  the  rate  of  cooling,  the 
head  of  metal  under  which  the  casting  is  made,  and  the  bulk 
of  the  casting. 

From  the  many  causes  by  which  the  strength  of  iron  may 
be  influenced,  it  is  very  difficult  to  judge  of  the  quality  of  a 
casting  by  its  external  characters  ;  however,  a  uniform  ap- 
pearance of  the  exterior  devoid  of  marked  inequalities  of  sur- 
face, generally  indicates  uniform  strength ;  and  large  castings 
are  generally  proportionally  weaker  than  small  ones. 


WROUGHT   OR   MALLEABLE   IRON. 

72.  Wrought,  or  Malleable  Iron,  in  its  perfect  condition, 
is  simply  pure  iron. 

It  generally  falls  short  of  such  condition  to  a  greater  or  less 
extent,  on  account  of  the  presence  of  the  impurities  referred 
to  in  a  previous  paragraph.  It  contains  ordinarily  more  than 
one-quarter  of  one  per  cent,  of  carbon. 


WROTJGHT-IBON.  35 

It  may  be  made  by  direct  reduction  of  the  ore,  but  it  is 
usually  made  from  cast-iron  by  the  process  called  pud- 
dling. 

Wrought-iron  is  tough,  malleable,  ductile  and  infusible  in 
ordinary  furnaces.  At  a  white  heat  it  becomes  soft  enough 
to  take  any  shape  under  the  hammer,  and  admits  of  being 
welded.  In  order  to  weld  two  pieces  together,  each  surface 
should  be  free  from  oxide.  If  there  be  any  oxide  present,  it 
is  easily  removed  by  sprinkling  a  little  sand  or  dust  or  borax 
over  the  surfaces  to  be  joined ;  either  of  these  forms  with  the 
rust  a  fusible  compound,  which  is  readily  squeezed  out  by  the 
hammering  or  rolling. 


Appearances  of  good  Wrought-iron. 

73.  The  fracture  of  good  wrought-iron  should  have  a  clear 
gray  color,  metallic  lustre,  and  a  fibrous  appearance.  A 
crystalline  structure  indicates,  as  a  rule,  defective  wrought- 
iron.  Blisters^  flaws^  and  cinder-holes  are  defects  due  to  bad 
manufacture. 

Strength. — The  strength  of  wrought-iron  is  very  variable, 
as  it  depends  not  only  on  the  natural  qualities  of  the  metal, 
but  also  upon  the  care  bestowed  in  forging,  and  upon  the 
greater  or  less  compression  of  its  fibres  when  it  is  rolled  or 
hammered  into  bars. 

Forms. — The  principal  forms  in  which  wrought-iron  is 
sent  to  market  are  Bar-iron,  Round-iron,  Hoop  and  Sheet- 
iron,  and  Wire. 

Bar-iron  comes  in  long  pieces  with  a  rectangular  cross- 
section,  generally  square,  and  is  designated  as  1  inch,  1J  inch, 
2  inch,  according  to  its  dimensions.  It  is  then  cut  and  worked 
into  any  shape  required. 

Bars  receive  various  other  forms  of  cross-section,  depend- 
ing upon  the  uses  that  are  to  be  made  of  them.  The  most 
common  forms  are  the  T,  H,  I,  and  L,  cross-sections,  called 
T-iron,  H -iron,  etc.,  from  their  general  resemblance  to  these 
letters,  and  one  whose  section  is  of  this  shape,  i— ',  called 
channel  iron.  The  section  like  an  inverted  U  is  frequently 
seen. 

Round  iron  comes  in  a  similar  form,  except  the  cross-sec- 
tion is  circular,  and  it  is  known,  in  the  same  way,  as  1  inch,  2 
inch,  etc. 

Hoop  and  Sheet-iron  are  modifications  of  bar-iron,  the 
thickness  being  very  small  in  comparison  with  the  width. 

Corrugated  iron  is  sheet-iron  of  a  modified  form,  by  which 


86  CTVTL   ENGINEERING. 

its  strength  and  stiffness  are 
greatly  increased.  The  dis- 
tance between  the  corruga- 
tions, A  B,  (Fig.  I.)  varies, 
being  3,  4,  or  5  inches  ;  the 
depth,  B  0,  being  about  one- 
fourth  A  B. 

Iron  Wire. — The  various  sizes  of  wire  might  be  consid- 
ered as  small  sizes  of  round-iron,  distinguished  by  numbers 
depending  on  the  dimensions  of  cross-section,  except  that  wire 
is  drawn  through  circular  holes  in  a  metal  plate,  while  round- 
iron  is  rolled^  to  obtain  the  requisite  cross-sections. 

The  numbers  run  from  0  to  36  ;  No.  0  wire  has  a  diameter 
equal  to  one-third  of  an  inch,  and  No.  36  one  equal  to  .004 
or  an  inch;  the  other  numbers  being  contained  between 
these,  and  the  whole  series  being  known  as  the  Birmingham 
Wire  Gauge. 

A  series  in  which  the  numbers  run  from  0  to  40,  the  ex- 
tremes being  nearly  the  same  as  that  just  given,  is  sometimes 
used.  It  is  known  as  the  American  Gauge. 


STEEL. 

74.  Steel,  the  hardest  and  strongest  of  the  metals,  is  a 
chemical  combination  of  iron  and  carbon,  standing  between 
wrought  and  cast-iron. 

No  sharp  dividing  line  can  be  drawn  between  wrought-iron 
and  steel,  based  on  the  proportions  of  carbon  present  in  the 
product.  The  differences  in  their  physical  properties  are 
largely  due  to  the  process  of  manufacture.  Many  of  the 
properties  peculiar  to  wrought-iron  have  been  found  to  dis- 
appear upon  melting  the  iron,  showing  that  they  were  the  re- 
sult of  the  manipulation  to  which  the  iron  was  subjected. 

The  term  steely-iron,  or  semi-steel,  has  been  applied  wher 
the  compound  contains  less  than  0.5  per  cent,  of  carbon ; 
steel,  when  containing  more  than  this,  and  less  than  2  per 
cent. ;  but  when  2  per  cent,  or  more  is  present,  the  compound 
is  termed  cast-iron,  as  before  stated. 

75.  Sieel  is  made  from  iron  by  various  processes,  which 
are  of  two  general  classes  ;  the  one  in  which  carbon  is  added 
to  malleable  iron ;  the  other  in  which  a  part  of  the  carbon  is 
abstracted  from  cast-iron.     Like  iron,  steel  is  seldom  pure, 
but  contains  other  substances  which,  as  a  rule,  affect  it  inju- 
riously.    There  are,  however,  some  foreign  substances  which, 
introduced  into  the  mass  during  manufacture,  have  a  bene- 


STEEL.  37 

ficial  effect  upon  the  steel  by  increasing  its  hardness  and 
tenacity  and  making  it  easier  to  forge  and  weld. 

76.  Steel, used  for  building  purposes,  is  made  generally  by 
one  of  three  processes : 

1.  By  fusion  of  blister  steel  in  crucibles ;   as  cast-steel ; 

2.  By  blowing  air  through  melted  cast-iron ;  as  Bessemer 
eteel;  or — 

3.  By  fusion  of  cast-iron  on  the  open  hearth  of  a  rever- 
beratory  furnace,  and  adding  the  proper  quantities  of  malle- 
able iron  or  scrap  steel ;  as  Siemens-Martin  steel. 

77.  The  different  kinds  of  steel  are  known  by  names  given 
them  either  from  their  mode  of  manufacture,  their  appear- 
ance, from  some  characteristic  constituent,  or  from  some  in- 
ventor's process;  such  are  German-steel,  blister-steel,  shear- 
steel,  cast-steel,  tilted-steel,  puddled-steel,    granulated-steel, 
Bessemer-steel,  etc. 

German-steel  is  produced  direct  from  certain  ores  of  iron, 
by  burning  out  a  portion  of  the  carbon  in  the  cast-iron  ob- 
tained by  smelting  the  ore.  It  is  largely  manufactured  in 
Germany,  and  is  used  for  files  and  other  tools.  It  is  also 
known  as  natural  steel. 

Blister-steel  is  made  by  a  process  known  as  " cementation" 
which  produces  a  direct  combination  of  malleable  iron  and 
carbon.  The  bars,  after  being  converted  into  steel,  are  found 
covered  with  blisters,  from  which  the  steel  takes  its  name.  It 
is  brittle,  and  its  fracture  presents  a  crystalline  appearance. 
It  sometimes  receives  the  name  of  bar-steel. 

Shear-steel  is  made  by  putting  bars  of  blister-steel  to- 
gether, heating  and  welding  them  under  the  forge-hammer, 
or  between  rolls ;  the  product  is  called  "  Shear-steel," 
"Double,"  "Single,"  or  "Half,"  from  the  number  of  times 
the  bars  have  been  welded  together.  It  is  used  for  tools. 

Cast-steel,  known  also  as  crucible-steel,  is  made  by  break- 
ing blistered  steel  into  small  pieces,  and  melting  it  in  close 
crucibles,  from  which  it  is  poured  into  iron  moulds.  The 
resulting  ingot  is  then  rolled  or  hammered  into  bars. 

Its  fracture  is  of  a  silvery  color,  and  shows  a  fine,  homoge- 
neous, even,  and  close  grain.  It  is  very  brittle,  acquires  ex- 
treme hardness,  and  is  difficult  to  weld  without  a  flux. 

This  is  the  finest  kind  of  steel,  and  the  best  adapted  for 
most  purposes  in  the  arts ;  but,  from  its  expensiveness,  it  is 
not  much  used  in  building. 

Tilted-steel  is  made  from  blistered  steel  by  moderately 
heating  the  latter  and  subjecting  it  to  the  action  of  a  tilt  or 
trip-hammer ;  by  this  means  the  tenacity  and  density  of  the 
steel  are  increased. 


38  CIVIL   ENGINEERING. 

Puddled-steel  is  made  by  puddling  pig-iron,  and  stopping 
the  process  at  the  instant  when  the  proper  proportion  of  car- 
bon remains. 

Granulated-steel  is  made  by  allowing  the  melted  pig-iron 
to  fall  into  water,  so  that  it  forms  into  grains  or  small  lumps ; 
the  latter  are  afterwards  treated  so  as  to  acquire  the  proper 
proportion  of  carbon,  and  are  then  melted  together. 

Bessemer-steel,  which  takes  its  name  from  the  inventor  of 
the  process,  is  made  by  direct  conversion  of  cast-iron  into 
steel.  This  conversion  is  effected  either  by  decarbonizing 
the  melted  cast-iron  until  only  enough  of  carbon  is  left  to 
make  the  required  kind  of  steel,  or,  by  removing  all  the  car- 
bon, and  then  adding  to  the  malleable  iron  remaining  in  the 
furnace  the  necessary  proportion  of  carbon  ;  the  resulting 
product  is  then  immediately  run  into  large  ingots. 

Siemens-Martin  steel  is  another  variety  of  steel  obtained 
directly  from  the  cast-iron,  and  takes  its  name  from  the  in- 
ventors of  the  process.  In  this  process,  the  carbon  is  not 
removed  by  a  blast  of  atmospheric  air,  as  in  the  Bessemer 
process,  but  by  the  oxygen  of  the  iron  ore  or  iron  scales,  etc., 
the  oxygen  being  freed  as  a  gas  during  combustion. 

In  each  of  the  last  two  processes,  the  temperature  is  so 
great  as  to  melt  wrought-iron  with  ease. 

There  are  other  kinds  of  steel,  possessing  certain  character- 
istics peculiar  to  themselves  or  claimed  for  them,  but  whose 
process  of  manufacture  is  not  publicly  known. 

78.  Hardening  and  Tempering. — Steel  is  more  granular 
than  iron,  and  is  much  more  easily  melted,  but  the  great  dif- 
ference between  them  is  the  capability  of  the  steel  to  become 
extremely  hard  and  elastic  when  tempered.     The  quality  of 
the  steel  depends  in  a  great  measure  on  the  operation  of  hard- 
ening and  tempering. 

It  is  hardened  by  being  heated  to  a  cherry-red  color,  and 
then  being  suddenly  cooled  by  being  plunged  into  some  cold 
liquid.  In  this  way  it  is  rendered  very  brittle,  and  so  hard 
as  to  resist  the  hardest  file.  To  give  elasticity,  it  is  tem- 
pered ;  this  is  done  by  heating  the  hardened  steel  to  a  cer- 
tain degree,  and  cooling  it  quickly ;  the  different  degrees  of 
heat  will  depend  upon  the  use  to  which  the  steel  is  to  be  put. 

These  qualities  of  hardness  and  elasticity  .adapt  it  for  vari- 
ous uses,  for  which  neither  cast  nor  wrought-iron.  would  bo 
suitable. 

DURABILITIY  OV  IRON  AND  STEEL. 

79.  Constructions  in  these  metals  are,  like  those  in  woorl, 
subject  to  the  same  general  conditions.     They  may  be  ex- 


PROTECTION   OF   IRON    WORK.  #$ 

posed  to  the  air  in  a  dry  place,  or  in  a  damp  place,  be  kept 
alternately  wet  and  dry,  or  be  entirely  immersed  in  fresh  or 
salt  water. 

Their  exposure  to  the  air  or  moisture,  especially  if  an  acid 
be  present,  is  followed  by  rusting  which  proceeds  with 
rapidity  after  it  once  begins.  The  corrosion  is  more  rapid 
under  exposure  to  alternate  wetness  and  dryness  than  in 
either  of  the  other  cases. 

Cast-iron  is  usually  coated  with  a  film  of  graphite  and 
ferrous  silicate,  produced  by  the  action  of  the  sand  of  the 
mould  on  the  melted  iron  ;  this  film  is  very  durable,  and, 
if  not  injured,  the  casting  will  last  a  long  time  without 
rusting. 

Iron  kept  in  a  constant  state  of  vibration  rusts  less  rapidly 
than  in  a  state  of  rest. 

Iron  completely  imbedded  in  brick-work  or  masonry  ia 
preserved  from  rust,  and  in  cathedrals  and  other  ancient 
buildings  it  has  been  found  in  good  condition  after  six  hun- 
dred years.  In  these  cases  the  iron  was  probably  protected 
by  the  lime  in  the  mortar,  the  latter  being  a  good  pre- 
servative. 

The  rapid  deterioration  of  iron-work  when  exposed  to  the 
air  and  to  moisture  makes  its  protection,  so  as  to  increase  its 
durability,  a  matter  of  great  importance. 


PROTECTION  OF  IRON-WORK. 

80.  The  ordinary  method,  used  to  protect  iron  from  rust, 
is  to  cover  its  surface  with  some  material  that  withstands  the 
action  of  the  air  and  moisture,  even  if  it  be  for  a  limited  time. 

The  following  are  some  of  the  methods : 

By  painting."—  The  surface  of  the  iron  is  covered  with  a 
coat  of  paint.  Eed  and  white  lead  paints,  ochreous  or  iron 
oxide  paints,  silicate  paints,  and  bituminous  paints,  all  are 
used.  For  this  purpose,  the  value  of  the  paint  depends 
greatly  upon  the  quality  of  the  oil  with  which  it  is  mixed. 
The  painting  must  be  renewed  from  time  to  time. 

By  japanning-. — The  iron  being  placed  in  a  heated  cham- 
ber, or  furnace,  the  paint  is  there  applied,  and  is  to  some 
extent  absorbed  by  the  iron,  forming  over  it  a  hard,  smooth, 
varnish-like  coating. 

By  the  use  of  coal-tar. — The  iron  is  painted  with  coal-tar 
alone  or  mixed  with  turpentine  or  other  substances ;  another 
method  consists  in  first  heating  the  iron  to  about  600°  Fahr., 
and  then  boiling  it  in  the  coal-tar. 


40  CIVIL   ENGINEERING. 

By  the  use  of  linseed  oil. — The  iron  is  heated,  and  the 
surface  while  hot  is  smeared  over  with  cold  linseed-oil. 

By  galvanizing. — This  term,  "galvanized  iron/'  is  ap- 
plied to  articles  of  iron  coated  with  zinc.  The  iron,  being 
thoroughly  cleaned  and  free  from  scale,  is  dipped  into  a  bath 
of  melted  zinc,  and  becomes  perfectly  coated  with  it.  This 
coating  protects  the  iron  from  direct  action  of  the  air  and 
moisture,  and  as  long  as  it  lasts  intact  the  iron  is  perfectly 
free  from  rust. 

COPPER. 

81.  This  metal  possesses  great  durability  under  ordinary 
exposure  to  the  weather,  and  from  its  malleability  and  tena- 
city is  easily  manufactured  into  thin  sheets  and  fine  wire. 

When  used  for  building  purposes,  its  principal  application 
is  in  roof-coverings,  gutters,  and  leaders,  etc.  Its  great 
expense,  compared  with  the  other  metals,  forms  the  chief 
objection  to  its  use. 

ZINC. 

82.  This  metal  is  used  much  more  than  copper  in  building, 
as  it  is  much  cheaper  and  is  exceedingly  durable.     Though 
zinc  is  subject  to  oxidation,  the  oxide  does  not  scale  off  like 
that  of  iron,  but  forms  an  impervious  coating,  protecting  the 
metal  under  it  from  the  action  of  the  atmosphere,  thus  ren- 
dering the  use  of  paint  unnecessary. 

In  the  form  of  sheets,  it  can  be  easily  bent  into  any  required 
shape. 

The  expansion  and  contraction  caused  by  variations  of  tem- 
perature are  greater  for  zinc  than  iron,  and  when  zinc  is  used 
for  roof -coverings,  particular  attention  must  be  paid  to  seeing 
that  plenty  oiptay  is  allowed  in  the  laps. 

Zinc,  before  it  is  made  into  sheets  or  other  forms,  is  called 
spelter. 

TIN. 

83.  This  metal  is  only  used,  in  building,  as  a  coating  for 
sheet-iron  or  sheet-copper,  protecting   their  surfaces  from 
oxidation. 

LEAD. 

84.  This  metal  was  at  one  time  much  used  for  roof -cover- 
ing, lining  of  tanks,  etc.     It  ip  now  almost  entirely  super- 
aeded  by  the  other  metals. 


TTNTTINQ   MATERIALS.  41 

It  possesses  durability,  but  is  wanting  in  tenacity ;  this 
requires  the  use  of  thick  sheets,  which  increase  both  the 
expense  and  the  weight  of  the  construction. 


ALLOTS. 

85.  An  alloy  is  a  compound  of  two  or  more  metals, 
mixed  while  in  a  melted  state.  Bronze,  gun-metal,  bell- 
metal,  brass,  pewter,  and  the  various  solders  are  some 
of  the  alloys  that  have  a  limited  application  to  building  pur- 
poses. 


CHAPTER  IV. 

UNITING  MATERIALS. 

86.  Structures  composed  of  wood  and  iron  have  their  dif- 
ferent portions  united  principally  by  means  of  straps  and 
pins  made  of  solid  materials;  in  some  cases,  especially  in 
the  smaller  structures,  a  cementing  material  is  used,  as  glue, 
etc. 

The  use  of  straps,  pins,  and  like  methods  of  fastenings 
will  be  described  under  the  head  of  FRAMING. 

Structures  composed  of  stone  have  their  different  portions 
united  principally  by  cementing  materials,  as  limes,  cements, 
mortars,  etc. 

GLUE. 

67.  Glue  is  a  hard,  brittle,  brownish  product  obtained  by 
boiling  to  a  jelly  the  skins,  hoofs,  and  other  gelatinous  parts 
of  animals,  and  then  straining  and  drying  it. 

When  gently  heated  with  water,  it  becomes  viscid  and 
tenacious,  and  is  used  as  a  uniting  material.  Although  pos- 
sessing considerable  tenacity,  it  is  so  readily  impaired  by 
moisture  that  it  is  seldom  used  in  engineering  constructions, 
except  for  joiner's  work. 


42  CIVIL   ENGINEERING. 

LIMES  AND  CEMENTS. 

LIMES. 

88.  If  a  limestone  be  calcined,  the  carbonic  acid  will  be 
driven  off  in  the  process,  and  the  substance  obtained  is  gen- 
erally known  as  lime. 

This  product  will  vary  in  its  qualities,  depending  on  the 
amount  and  quality  of  the  impurities  of  the  limestone.  As 
a  building  material,  the  products  are  divided  into  three  prin- 
cipal classes : 

1.  Common  or  fat  lime. 

2.  Hydraulic  lime. 

3.  Hydraulic  cement. 

Common  lime  is  sometimes  called  air-lime,  because  a  paste 
made  from  it  with  water  will  harden  only  in  the  air. 

Hydraulic  lime  and  cement  are  also  called  water  limes 
and  cements,  because  a  paste  made  from  either  of  them 
with  water  has  the  valuable  property  of  hardening  under 
water. 

The  principal  use  of  the  limes  and  cements  in  the  engineer's 
art  is  as  an  ingredient  in  the  mortars  and  concretes. 

Varieties  of  Limestone. 

89.  The  majority  of  limestones   used  for  calcination  are 
not  pure  carbonates,  but  contain  various  other  substances,  the 
principal  of  which  are  silica,  alumina,  magnesia,  etc. 

If  these  impurities  be  present  in  sufficiently  large  quan- 
tities, the  limestone  will  yield  on  calcination  a  product  pos- 
sessing hydraulic  properties. 

Limestones  may  therefore  be  divided  into  two  classes,  or- 
dinary and  hydraulic,  according  as  the  product  obtained  by 
calcination  does  or  does  not  possess  hydraulic  properties. 

90.  Ordinary  Limestone. — A  limestone  which  does  not 
contain  more  than  ten  per  cent,  of  these  impurities,  produces 
common  lime   when   calcined.     White   chalk,  and  statuary 
marble,  are  specimens  of  pure  limestone. 

91.  Hydraulic  Limestones. — Limestones  containing  more 
than  ten  per  cent,  of  these  impurities  are  called  hydraulic 
limestones,  because  they  produce,  when  properly  calcined,  a 
lime  having  hydraulic  properties. 


HYDRAULIC   LIMESTONES.  43 

The  hydraulic  limestones  are  subdivided  into  silicious, 
argillaceous,  magnesian  and  argillo-magnesian,  according 
to  the  nature  of  the  predominating  impurity  present  in  the 
stone. 

Physical  Characters  and  Tests  of  Hydraulic  Limestones. 

92.  The  simple  external  characters  of  a  limestone,  as  color, 
texture,  fracture,  and  taste,  are  insufficient  to  enable  a  person 
to  decide  whether  it  belongs  to  the  hydraulic  class. 

Limestones  are  generally  of  some  shade  of  drab  or  of  gray, 
or  of  a  dark  grayish  blue ;  have  a  compact  texture,  even  or 
conchoidal  fracture,  a  clayey  or  earthy  smell  and  taste.  Al- 
though the  hydraulic  limestones  are  usually  colored,  still  the 
stone  may  happen  to  be  white,  from  the  combination  of  lime 
with  a  pure  clay. 

The  difficulty  of  pronouncing  upon  the  class  to  which  a 
limestone  belongs  renders  necessary  a  resort  to  chemical 
analysis  and  experiment. 

To  make  a  complete  chemical  analysis  of  a  limestone  re- 
quires more  skill  in  chemical  manipulations  than  engineers 
usually  possess ;  but  a  person  who  has  the  ordinary  element- 
ary knowledge  of  chemistry  can  ascertain  the  quantity  of 
clay  or  of  magnesia  contained  in  a  limestone,  and  (know- 
ing this)  can  pronounce,  with  tolerable  certainty,  as  to  the 
probabilities  of  its  possessing  hydraulic  properties  after  cal- 
cination. 

Having  from  the  proportions  ascertained  that  the  stone  will 
probably  furnish  a  lime  with  hydraulic  properties,  a  sample 
of  it  should  be  submitted  to  experiment.  The  only  apparatus 
required  for  this  purpose  is  a  crucible  that  will  hold  about  a 
pint,  and  a  mortar  and  pestle.  The  bottom  as  well  as  the  top 
or  cover  of  the  crucible  should  be  perforated  to  give  an  up- 
ward current  of  air  and  allow  the  carbonic  acid  to  escape. 
The  stone  to  be  tested  is  broken  into  pieces  as  nearly  the 
same  size  as  possible,  not  exceeding  three-fourths  of  an  inch 
cube,  and  placed  in  the  crucible.  When  more  than  one  speci- 
men is  to  be  tried,  and  a  comparison  between  them  made, 
there  should  be  several  crucibles.  Access  being  had  to  an 
anthracite  coal-fire  in  an  open  grate,  or  to  any  other  steady 
fire,  the  crucibles  are  embedded  in  and  covered  with  glowing 
coals,  so  that  the  top  and  bottom  portions  of  their  contents 
will  attain  simultaneously  a  bright- red  heat,  each  crucible 
containing  as  nearly  as  possible  the  same  quantity  of  stone. 
If  there  be  only  one  crucible,  two  or  three  of  the  fragments 
are  removed  in  forty-five  minutes  after  the  stone  has 


44  CIVIL  ENGINEERING. 

reached  a  red  heat ;  in  forty-five  minutes  afterwards  two  or 
three  more  are  taken  out,  and  this  repeated  for  f our  ^  and  a 
half  and  perhaps  six  hours,  which  time  will  be  sufficient  to 
expel  all  the  carbonic  acid.  If  there  be  several  crucibles, 
they  themselves  may  be  removed  in  the  same  order.  By  this 
means  we  will  have  some  samples  of  the  stone  that  are  burnt 
too  much,  some  not  enough,  and  some  of  a  class  between 
them. 

The  specimen,  if  a  cement,  will  not  slake  when  sprinkled 
with  water.  By  reducing  it  to  a  powder  in  the  mortar,  mix- 
ing it  to  a  stiif  paste  with  water,  immersing  it  in  fresh  or  salt 
water,  and  noting  the  time  of  setting  and  the  degree  of  hard- 
ness it  attains,  an  approximate  value  of  the  cement  may  be 
obtained. 

Calcination  of  Limestones. 

93.  As  the  object  in  burning  limestone  is  to  drive  ofF  the 
water  and  carbonic  acid  from  the  limestone,  many  devices 
have  been  used  to  effect  it.     A  pile  of  logs  burning  in  the 
open  air,  on  which  the  limestone  or  oyster-shells  are  thrown, 
has  been  frequently  used  to  obtain  common  lime.    It  is,  how- 
ever, generally  manufactured  by  burning  the  limestone  in  a 
kiln  suitably  constructed  for  the  purpose. 

94.  Kilns  are  divided  into  two  classes :  1st,  the  intermit- 
tent kilns,  or  those  in  which  the  fuel  is  all  at  the  bottom, 
and  the  limestone  built  up  over  it;  and,  2d,  the  perpetual 
or  draw  kiln,  in  which   the  fuel  and   the  limestone  are 
placed  in  the  kiln  in  alternate  layers.     The  fuel  used  is 
either  wood  or  coal.     In  the  first  class  one  charge  of  lime  is 
burned  at  a  time,  and,  when  one  burning  is  complete,  the  kiln 
is  completely  cleared  out  previous  to  a  second  ;  while  in  the 
latter  class  fresh  layers  of  fuel  and  limestone  are  added  at 
the  top  as  the  lime  is  drawn  out  at  the  bottom. 

The  shapes  given  to  the  interiors  of  kilns  are  very  different. 
The  object  sought  is  to  obtain  the  greatest  possible  uniform 
heat  with  the  smallest  expenditure  of  fuel,  and  for  this  pur- 
pose thick  walls  are  necessary  to  prevent  loss  of  heat  by  radi- 
ation. 

95.  Intermittent  Kilns. — The  simplest  form  of  kiln  is 
that  represented  in  Fig  2,  in  which  wood  is  used  for  fuel.    It 
has  a  circular  horizontal  cross -section,  and  is  made  of  ham- 
mered limestone  without  mortar. 

The  cut  represents  a  vertical  section  through  the  axis  and 
arched  entrance  communicating  with  the  interior  of  a  kiln 
for  burning  lime  with  wood ;  0,  <?,  c,  large  pieces  of  limestone 


LIME-KILNS. 


45 


forming  the  arch  upon  which  the  mass  of  limestone  rests ;  A , 
arched  entrance  communicating  with  the  interior. 


FIG.  2. 

It  is  usually  placed  on  the  side  of  a  hill,  so  that  the  top 
may  be  accessible  for  charging  the  kiln. 

The  largest  pieces  of  the  limestone  to  be  burned  are 
formed  into  an  arch,  <?,  <?,  0,  and  above  this  the  kiln  is  filled 
by  throwing  the  stone  in  loosely  from  the  top,  the  largest 
stones  first  and  smaller  ones  afterwards,  heaping  them  up,  as 
shown  in  the  figure.  The  fuel  is  supplied  through  the 
arched  entrance,  A. 

The  circular  seems  the  most  suitable  form  for  the  horizon- 
tal sections  of  a  kiln,  both  for  strength  and  for  economy  of 
heat.  Were  the  section  the  same  throughout,  or  the  form  of 
the  interior  of  the  kiln  cylindrical,  the  strata  of  stone,  above 
a  certain  point,  would  be  very  imperfectly  burned  when  the 
lower  strata  were  calcined  just  enough,  owing  to  the  rapidity 
with  which  the  inflamed  gases  arising  from  the  combustion 
are  cooled  by  coming  into  contact  with  the  stone.  To  pro- 
cure, therefore,  a  temperature  which  shall  be  nearly  uniform 
throughout  the  heated  mass,  the  horizontal  sections  of  the 
kiln  should  gradually  decrease  from  the  point  where  the 
flame  rises,  which  is  near  the  top  of  the  dome  of  broken 
stone,  to  the  top  of  the  kiln.  This  contraction  of  the  hori- 
zontal section  from  the  bottom  upward  should  not  be  made 


46  CIVIL   ENGINEERING. 

too  rapidly,  <ts  the  draught  would  be  thereby  injured  and  the 
capacity  of  the  kiln  too  much  diminished ;  and  in  no  case 
should  the  area  of  the  top  opening  be  less  than  about  one- 
fourth  the  area  of  the  section  taken  near  the  top  of  the  dome. 
The  proportions  between  the  height  and  mean  horizontal  sec- 
tion will  depend  on -the  texture  of  the  stone,  the  size  of  the 
fragments  into  which  it  is  broken  for  burning,  and  the 
greater  or  less  ease  with  which  it  vitrifies. 

A  better  kiln  than  the  one  shown  in  Fig.  2  will  be  obtained 
by  giving  an  ovoidal  shape  to  the  interior,  lining  it  with  fire- 
brick, substituting  for  the  arch  of  limestones  a  brick  arch 
with  openings  to  admit  a  free  circulation  of  air,  so  as  to 
secure  the  necessary  draught,  and  arranging  it  with  a  fire- 
grate. 

The  management  of  the  burning  is  a  matter  of  experience. 
For  the  first  eight  or  ten  hours  the  fire  should  be  carefully 
regulated,  in  order  to  bring  the  stone  gradually  to  a  red  heat. 
By  applying  a  high  heat  at  first,  or  by  any  sudden  increase 
of  it  before  the  mass  has  reached  a  nearly  uniform  tempera- 
ture, the  stone  is  apt  to  shiver,  and  to  choke  the  kiln  by  stop- 
ping the  voids  between  the  courses  of  stone  which  form  the 
dome.  After  the  stone  is  brought  to  a  red  heat,  the  supply 
of  fuel  should  be  uniform  until  the  end  of  the  calcination. 
Complete  calcination  is  generally  indicated  by  the  diminu- 
tion which  gradually  takes  place  in  the  mass,  and  wThich,  at 
this  stage,  is  about  one-sixth  of  the  primitive  volume ;  by 
the  broken  appearance  of  the  stone  which  forms  the  dome, 
and  by  the  interstices  being  choked  up  with  fragments  of 
the  burnt  stone;  and  by  the  ease  with  which  an  iron 
bar  may  be  forced  down  through  the  burnt  stone  in  the 
kiln.  When  these  indications  of  complete  calcination  are 
observed,  the  kiln  should  be  closed  for  ten  or  twelve  hours 
to  confine  the  heat  and  finish  the  burning  of  the  upper 
strata. 

The  defects  of  the  intermittent  kilns  are  the  great  waste 
of  fuel,  and  that  the  stone  nearest  the  fire  is  liable  to 
be  injured  by  over-burning  before  the  top  portions  are  burnt 
enough. 

96.  Perpetual  Kilns. — Perpetual  kilns  are  intended  to 
remedy  these  defects,  especially  the  waste  of  heat.  A  simple 
form  of  a  kiln  of  tLis  class  is  shown  in  Figs.  3  and  4.  The 
interior  is  an  inverted  frustum  of  a  cone  from  five  to  five 
and  a  half  feet  in  diameter  at  bottom,  and  nine  or  ten  at 
top,  and  thirteen  or  fourteen  high.  It  is  arranged  with 
three  arched  entrances,  a,  a,  «,  for  drawing  the  lime,  and  they 
are  arranged  with  doors  for  regulating  the  draught. 


IJME-KILN8. 


Fig.  3  represents  a  horizontal  section  made  near  the  base, 
and  Fig.  4,  a  vertical  section  on  A  B,  through  the  axis 
the  kiln. 


FIG.  3.  FIG.  4. 

These  kilns  are  arranged  for  burning  by  first  placing  a 
layer  of  light  wood  at  the  bottom,  then  a  layer  of  coal,  and 
then  a  layer  of  limestone.  Layers  of  coal  and  limestone 
follow  alternately  until  the  kiln  is  filled.  The  lower  layer  is 
ignited,  and  as  the  burnt  mass  settles  down,  and  the  lime 
near  the  bottom  is  sufficiently  burnt,  the  drawing  com- 
mences. 

Wood  is  not  as  convenient  a  fuel  as  coal  for  this  kiln,  the 
principal  objections  being  the  difficulty  of  obtaining  the 
pieces  always  the  same  size  and  of  distributing  it  uniformly 
in  the  layers. 

The  perpetual  kiln  is  more  economical  than  the  intermit- 
tent in  the  use  of  fuel,  but  requires  more  skill  and  caution 
in  its  management. 

The  perpetual  kiln  invented  by  Mr.  C.  D.  Page,  of  Koches- 
ter,  N.  Y.,  is  extensively  used  in  the  western  part  of  New 
York  and  in  Maine.  It  is  known  as  a  perpetual  flame 
or  furnace  kiln,  is  arranged  for  either  wood  or  coal,  anthra- 
cite or  bituminous,  and  avoids  the  defects  arising  from  mix- 
ing the  fuel  and  stone  together. 

The  foregoing  are  types  of  the  kilns  used  for  burning  lime- 
stones, whether  the  product  is  to  be  common  lime  or  hydrau- 
lic cement.  The  perpetual  kiln  is  generally  used  for  burning 
limestone  for  cement. 

Figures  5  and  6  represent  vertical  sections  through  the 
axis  of  the  kiln  and  draw-pit  of  the  ordinary  perpetual 
kilns  used  in  the  United  States  for  burning  lime-stone  for 
cement. 

Fig.  5  represents  the  section  of  the  kiln  used  in  Maryland 


CIVIL  ENGINEERING. 


and  Virginia ;  and  Fig.  6  of  those  preferred  in  New  York 
and  Ohio. 


20' 


' 


FIG.  5. 


FIG.  6. 


97.  The  great  object  of  a  kiln  is  to  give  a  cement  of  good 
and  homogeneous  quality  with  economy  of  fuel.  This  uni- 
formity of  product  is  not  obtained  from  either  the  intermit- 
tent or  perpetual  kilns  ordinarily  used ;  some  of  the  stone 
being  over-burnt,  while  other  portions,  usually  the  largest 
fragments,  are  under-burnt,  in  some  cases  partly  raw  inside. 
Both  over  and  under-burnt  pieces  are  difficult  to  reduce  to 
powder,  and  materially  affect  the  quality  of  the  cement.  It 
is  very  evident  that  dissimilar  stones  should  not  be  burned 
together  in  the  same  kiln. 

V  arious  kilns  have  been  devised  to  remedy  all  defects,  and 
still  be  economical  of  fuel.  The  perpetual  flame  or  furnace 
kiln  of  Page,  before  named,  and  the  annular  or  ring  kiln,  of 
which  the  Hoffman  is  a  type,  are  noted  examples. 


Products  of  Calcination  of  Limestones. 

98.  The  products  obtained  by  calcination  have  been  divid- 


COMMON   AND  HYDRAULIC   LIMES.  4:9 

ed  into   common  lime,  hydraulic  lime,  and  hydraulic 
cement. 

'   COMMON   LIME. 

99.  Lime,  common  lime,  air-lime,  quick-lime,  caustic 
lime  (synonymous  terms)  is  a  calcium  monoxide,  produced 
whenever  any  variety  of  pure  or  nearly  pure  limestone  is 
calcined  with  a  heat  of  sufficient  intensity  and  duration  to 
expel  the  carbonic  acid  [carbon  dioxide].     It  is  amorphous, 
infusible,  somewhat  spongy,  highly  caustic,  has  a  specific 
gravity  of  2.3,  and  possesses  great  avidity  for  water.     On 
being  mixed  with  an  equivalent  of  water,  the  water  is  rapidly 
absorbed  with  evolution  of  great  heat ;  the  lime  swells,  bursts 
into  pieces,  and  finally  crumbles  into  a  fine  white  powder,  of 
which  the  volume  is  from  two  and  a  half  to  three  and  a  half 
times  that  of  its  original  bulk.     In  this  condition  the  lime  is 
said  to  be  slaked  and  ready  for  use  in  making  mortar. 

The  limestones  which  furnish  the  lime  of  commerce  are 
seldom  pure,  the  impurities  amounting  sometimes  to  nearly 
ten  per  cent.  The  purer  the  limestone,  the  larger  is  the  in- 
crease of  volume  or  the  growth  of  the  lime  in  slaking,  and 
the  more  unctuous  to  the  sight  and  touch  is  the  paste  made 
therefrom.  For  this  reason  the  limes  made  from  the  purer 
stones  are  often  called  fat  or  rich  limes,  as  distinguished 
from  those  known  as  poor  or  meagre  limes,  and  wnich  are 
made  from  stones  containing  considerable  impurity. 

The  poor  limes  are  seldom  reduced  to  an  impalpable,  ho- 
mogeneous powder  by  slaking,  and  are  characterized  by  less 
growth.  They  yield  a  thin  paste,  and  are  principally  used 
as  fertilizers.  If  it  be  necessary  to  use  them  for  building 
purposes,  they  should  be  reduced  to  a  fine  powder  by  grind- 
ing ;  however,  they  should  never  be  used  if  it  be  possible  to 
avoid  so  doing. 

HYDRAULIC  LIMES. 

100.  These  occupy  an  intermediate  place  between  the  com- 
mon limes  and  the  hydraulic  cements.     They  are  obtained  by 
calcining  limestones  in  which  the  impurities,  silica,  alumina, 
magnesia,  etc.,  range  from  ten  to  twenty  per  cent.     When 
ten  to  twenty  per  cent,  of  impurity  is  chiefly  clay,  and  is 
homogeneously  mixed  with  the  carbonate  of  lime,  the  stones 
are  known  as  argillaceous  hydraulic  limestones;  and  when 
this  proportion  of  impurity  is  chiefly  of  silica,  they  are  called 
silicious  hydraulic  limestones. 


50  CIVIL   ENGINEERING. 

Hydraulic  lime,  upon  being  mixed  with  water,  slakes  more 
slowly  than  the  meagre  limes,  suffers  a  slight  elevation  of  tem- 
perature accompanied  by  little  or  no  vapor,  and  an  increase 
of  volume  rarely  exceeding  one-third  of  its  original  bulk.  A 
paste  made  from  this  lime  after  it  has  been  slaked,  hardens 
under  water. 

It  is  not  manufactured  in  the  United  States,  nor  is  it  known 
if  there  be  in  the  United  States  any  deposits  of  the  argilla- 
ceous hydraulic  limestones  capable  of  furnishing  good  hydrau- 
lic lime. 

Hydraulic  lime,  made  from  the  argillaceous  limestone,  is 
manufactured  in  several  localities  in  France,  notably  at  Seilley, 
about  seventy  miles  from  Paris. 

The  best  type  of  hydraulic  lime  from  the  silicious  lime- 
stone is  that  known  as  the  hydraulic  lime  of  Teil,  from  the 
quarries  of  Teil  on  the  Rhone,  Department  of  Ardeche,  France. 


HYDRAULIC    CEMENT. 

101.  If  the  limestone  contain  more  than  20  per  cent,  and 
less  than  40  of  the  impurities  before  named,  the  product  ob- 
tained by  calcination  is  an  hydraulic  cement. 

Hydraulic  cement  will  not  slake,  and  a  paste  made  from  it 
with  water  will  harden  or  set  under  water.  The  rapidity  of 
setting  and  the  degree  of  hardness  will  vary  with  the  homo- 
geneous character  of  the  stone,  the  proportions  into  which  the 
clay  and  lime  enter,  and  the  intensity  and  duration  of  the 
burning. 

The  effect  of  heat  on  lime-stones  varies  with  the  constituent 
elements  of  the  stone.  The  pure  limestones,  and  those  in 
which  the  only  impurity  is  not  more  than  22  per  cent,  of 
clay,  will  stand  a  high  degree  of  temperature,  losing  their 
carbouic  acid  and  water  without  fusing,  while  the  others  become 
more  or  l^ss  vitrified  when  the  temperature  much  exceeds  a 
red  heat. 

102.  Thne  are  two  general  classes  of  hydraulic  cements, 
the  slow  and  the  quick  setting. 

If  the  limestone  contain  at  least  20,  and  not  more  than  22 
per  cent,  of  clay,  and  is  burned  at  high  heat,  the  product  is  a 
heavy,  slow-setting  cement. 

If  there  be  from  27  to  30  per  cent,  of  clay,  aud  even  as 
high  as  35  in  some  cases,  and  the  burning  be  moderate,  the 
result  is  a  light,  quick-setting  cement. 

The  stone  that  might,  with  proper  burning,  have  yielded  a 
slow-setting  cement,  will,  if  burned  at  a  moderate  heat,  pro- 


FOZZUOLANAS.  51 

duce  a  light,  quick-setting  cement.  The  Roman  cement,  that 
of  Yassy,  and  the  hydraulic  cements  ordinarily  made  in  the 
United  States,  are  examples  of  the  quick-setting  class. 

The  proportion  existing  between  the  impurities  and  the 
lime  exercises  a  controlling  influence  on  the  properties  of  the 
hydraulic  cements,  and,  when  the  proportion  of  lime  is  less 
than  40  per  cent.,  the  stone  will,  upon  calcination,  produce 
neither  lime,  hydraulic  lime,  nor  hydraulic  cement. 

POZZUOLANA8. 

103.  If  clay  be  present  in  excess  in  the  limestone,  the  prod- 
uct obtained*  by  calcination  is    known  as  calcareous  poz- 
zuolana,  and  when  there  is  10  per  cent,  of  lime  or  less,  simply 
pozzuolana. 

Pozzuolana^  which  gives  the  name  to  this  class,  is  a  kind 
of  tufa,  of  volcanic  origin,  containing  about  9  per  cent,  of  lime, 
45  of  silica,  15  of  alumina,  and  the  rest  of  other  impurities, 
and  is  found  near  Rome,  in  Italy. 

It  was  originally  discovered  at  the  foot  of  Mount  Vesuvius, 
near  the  village  or  Pozzuoli,  whence  its  name. 

It  sometimes  exists  in  a  coherent  form,  but  more  frequently 
in  powder  of  coarse,  sharp,  and  angular  grains,  generally 
brown  in  color,  running  to  reddish.  If  lime  be  added  to 
supply  the  deficiency,  hydraulic  properties  can  be  imparted 
to  the  mortar  made  from  it.  This  fact  has  been  known  for 
centuries,  and  Vitruvius  and  Pliny  both  speak  of  its  high 
qualities  and  its  use  by  the  Romans  in  the  marine  construc- 
tions of  their  time. 

104.  Artificial  Pozzuolanas. — They  may  be  prepared  by 
grinding  well-burnt  bricks  to  powder,  or  by  burning  brick- 
clay  and  grinding  it. 

Trass  or  Terras. 

105.  This  substance  resembles  pozzuolana,  is  used  in  the 
same  manner,  and  possesses  the  same  properties.     It  is  used 
in  Holland,  being  principally  obtained  from  Bonn  and  An- 
dernach,  on  the  Rhine,  below  Coblentz.    If  any  deposits  exist 
in  the  United  States,  they  are  not  known. 

MANUFACTURE  OF  LIMES  AND  CEMENTS. 

106.  Common  lime  is  obtained,  as  already  stated,  by  the  cal- 
cination of  limestones,  in  which  there  is  less  than  ten  per  cent 


52  CIVIL  ENGINEERING. 

of  impurities;   the  limestone  is  burnt  in  kilns,  and  in  the 
manner  already  described. 


Manufacture  of  Hydraulic  Limes. 

107.  Hydraulic  lime  is  not  manufactured  in  the  United 
States. 

In  France  it  is  made  by  burning  the  stone  in  a  suitable 
kiln  at  a  heat  sufficient  to  drive  off  the  carbonic  acid.  While 
Btill  warm  from  the  kiln,  the  stone  is  sprinkled  with  from  15 
to  20  per  cent,  of  its  own  weight  of  water,  care  being  taken 
not  to  use  enough  to  convert  any  portion  of  it  into  paste. 
The  slaking  soon  begins,  and  the  stone  falls  to  pieces.  The 
mass  in  then  thrown  together  in  large  heaps,  and  left  undis- 
turbed for  six  or  eight  days.  It  is  then  screened  with  sieves 
of  25  to  30  fine  wires  to  the  lineal  inch. 

The  portion  which  passes  the  screen  is  hydraulic  lime. 


Manufacture  of  Hydraulic  Cements. 

108.  The  hydraulic  cements  produced  at  a  low  heat  are 
light  in  weight  and  quick-setting,  and  the  mortars  and  con- 
cretes made  from  them  never  attain  the  strength  and  hard- 
ness of  those  made  from  the  heavy  and  slow-setting  cements 
produced  by  burning  with  heat  of  great  intensity  and  duration. 


Hydraulic  Cements  from  Argillaceous  Limestones. 

109.  Heavy,  Slow-setting  Cements.— The  best  example 
of  this  class  is  the  Portland  cement,  which  is  made  from 
argillaceous  limestones,  containing  from  20  to  22  per  cent. 
of  clay,  or  from  an  artificial  mixture  of  carbonate  of  lime 
and  clay  in  similar  proportions.  JSTineteen-twentieths  of  all 
the  Portland  cement  of  the  present  day  is  artificial.  It  is  manu- 
factured extensively  throughout  Europe,  either  by  the  -wet 
process,  as  in  England,  or  the  dry  process,  as  in  Germany. 


The  Wet  Process. 

110.  The  wet  process,  as  practised  by  the  works  near 
London,  is  as  follows :  The  carbonate  of  lime  is  furnished  by  the 


CEMENTS.  53 

chalks,  and  the  clay  is  from  the  shores  of  the  Medway  and 
Thames  and  adjoining  marshes;  both  the  chalk  and  clay  are 
practically  pure. 

First.  The  clay  and  chalk  in  the  proper  proportions,  about 
one  to  three  by  weight,  are  mixed  together  in  a  circular  wash- 
mill,  so  arranged  as  to  thoroughly  pulverize  the  chalk  and 
convert  the  whole  into  a  semi-fluid  paste. 

Second.  When  the  thorough  mixture  is  effected,  the  liquid, 
resembling  whitewash  in  appearance,  is  drawn  off  into  reser- 
voirs, where  it  is  left  to  settle.  The  heavier  material,  or  raw 
cement,  settles  to  the  bottom,  and  then  the  surplus  water  which 
is  clear  is  removed.  Samples  are  taken  from  the  reservoirs 
from  time  to  time  and  tested.  If  any  error  be  discovered  in 
the  proportions,  it  is  corrected. 

Third.  When  by  evaporation  the  mixture  has  attained  the 
consistency  of  hard  butter  or  stiff  clay,  it  is  removed  from  the 
reservoirs  to  rooms  artificially  heated,  and  is  spread  out  for 
further  drying. 

Fourth.  After  it  has  dried  sufficiently,  it  is  burned  in  suit- 
able kilns  at  a  white  heat,  just  below  the  point  of  vitrif action. 

Fifth.  The  product  is  then  ground  between  ordinary  mill- 
stones to  a  powder  of  the  necessary  fineness.  It  is  then  ready 
for  use. 

0 

The  Dry  Process. 

111.  The  dry  process,  as  practised  in  Germany,  is  as  fol 
lows :  The  carbonate  of  lime  and  clay  are  first  kiln-dried  at  the 
temperature  of  212°  Fahr.,  then  mixed  together  in  the  proper 
proportions,  between  20  and  23  per  cent,  of  clay  to  between 
80  and  77  per  cent,  of  the  carbonate  of  lime,  and  reduced  to 
a  fine  powder.     This  powder  is  then  made  into  a  stiff  paste, 
and  then  into  blocks  about  the  size  of  bricks.     These  bricks 
are  dried  and  then  burnt  at  a  high  heat  in  a  kiln,  and  then 
ground  to  powder  as  in  the  preceding  case. 

112.  It  is  an  easy  matter  to  pulverize  the  materials,  either 
wet  or  dry,  mix  them,  and  then  grind  the  burnt  stone  to  a 
powder.     The  difficult  part  is  the  proper  application  and 
management  of  the  heat  in  burning.     The  mysterious  con- 
version which  takes  place  in  the  kiln  under  a  heat  of  suffi- 
cient intensity  to  make  glass,  is  to  some  extent  beyond  our  con- 
trol, and  to  a  great  extent  beyond  our  knowledge. 

In  whatever  manner  apparently  homogeneous  limestones 
may  be  exposed  to  burning  at  a  high  temperature,  it  is  impos- 
sible to  avoid  the  vitrifaction  of  some  layers  containing  an 


54  CIVIL  ENGINEERING. 

excess  of  silica,  and  to  prevent  others  not  having  enough  clay 
from  producing  cements  having  lime  in  excess.  For  this  rea- 
son an  artificial  mixture  of  clay  and  carbonate  of  lime  is  gen- 
erally relied  upon  for  Portland  cement. 

The  superior  quality  of  Portland  cement  appears  to  depend 
greatly  upon  the  presence  of  the  double  silicate  of  lime  and 
alumina,  which  is  formed  only  at  a  high  heat. 

If  an  argillaceous  limestone  does  not  contain  at  least  20 
per  cent.  o£  clay,  the  carbonate  of  lime  is  in  excess,  and  the 
high  heat  necessary  to  produce  a  heavy,  slow-setting  cement 
fails  to  produce  the  semi-fusion  which  is  the  characteristic 
of  such  a  cement. 

113.  Light,  Quick-Setting  Cements. — If  the  limestone 
contain  more  than  23  per  cent,  of  clay,  as  great  as  30  per  cent, 
and  exceptionally  as  high  as  35  per  cent.,  and  the  calcination 
be  kept  below  the  point  of  vitr  if  action,  it  will  yield  a  light, 
quick-setting  cement.     The  result  appears  to  be  silicate  and 
aluminate  of  lime  with  uncombined  clay,  but  more  especially 
silica,  which,  being  inert,  adulterates  and  injures  the  cement. 

A  cement  of  this  kind  sets  quickly  under  water,  but  is  far 
inferior  to  the  Portland  cement  in  hardness  and  final  strength. 
Those  of  Yassy,  Grenoble,  etc.,  in  France,  and  the  English 
and  French  Roman  cements  made  from  nodules  of  septariaj 
belong  to  this  class. 

This  kind  of  cement  may  be  made  artificially,  and  was 
quite  extensively  used  before  the  superior  qualities  oi  the 
Portland  cement  were  known. 

If  the  limestone  contain  more  than  23  per  cent,  of  clay  ho- 
mogeneously distributed  through  the  mass,  and  is  burnt  with 
a  heat  of  great  intensity  and  duration,  similar  to  that  required 
to  produce  Portland  cement,  it  generally  fuses  into  a  species 
of  slag  or  glass,  and  is  worthless  as  a  cement. 

Hydraulic  Cements  from  Argillo-Magnesian  Limestones. 

114.  The  natural  hydraulic  cements  of  the  United  States 
are  made  from  the  limestones  whose  principal  ingredients 
are  carbonate  of  lime,  carbonate  of  magnesia,  and  clay. 

The  usual  process  of  manufacture  is  to  break  the  stone  into 
pieces  not  exceeding  twelve  or  fifteen  pounds  in  weight,  and 
burn  them  in  an  ordinary  kiln,  either  intermittent  or  perpet- 
ual, the  latter  being  generally  used  when  coal  is  the  fuel. 
After  being  burnt,  the  fragments  are  crushed  by  suitable 
machinery,  and  then  reduced  to  a  powder  by  grinding.  The 
powder  is  then  packed  in  barrels  and  sent  to  market. 


CEMENTS.  55 

These  limestones  cannot  be  burned  with  the  intensity  and 
duration  of  heat  necessary  to  make  Portland  cement,  without 
fusing  into  a  slag  destitute  of  hydraulic  properties.  Like 
those  argillaceous  limestones  which  have  more  than  23  per 
cent,  of  clay,  they  will,  if  properly  burned,  produce  a  light, 
quick-setting  cement,  which  is  a  silicate  and  aluminate  of 
lime  and  magnesia. 

The  cements  from  the  valley  of  Rondout  Creek,  Ulster 
County,  N.  Y.,  known  as  Rosendale  cement;  from  near 
Shepherdstown,  Ya.  ;  Cumberland,  Md. ;  Louisville,  Ky. ; 
Sandusky,  Ohio ;  Utica,  111. ;  and  other  localities  in  the 
U.  S.,  are  made  from  this  stone,  and  belong  to  this  class  of 
cements. 

The  Rosendale  cement,  which  is  the  most  valuable  of  them, 
will,  under  favorable  circumstances,  attain  about  one-third 
of  the  ultimate  strength  and  hardness  of  the  Portland  ce- 
ment. 

Hydraulic  Cements  from  Magnesian  Limestones. 

115.  Pure  carbonate  of  magnesia,  known  as  magnesite, 
when  burned  at  a  cherry-red  heat,  reduced  to  powder,  and 
made  in  a  paste,  possesses  hydraulic  properties.  If  the  pow- 
der be  mixed  in  a  paste  with  magnesium  chloride — or,  a  very 
good  substitute  for  it,  bittern,  the  residue  of  sea-water  after 
the  salt  has  been  separated  by  crystallization — a  cement  is 
made  superior  in  strength  and  hardness  to  any  other  known, 
not  excepting  even  the  Portland.  This  calcined  magnesite 
has  been  patented  under  the  name  of  Union  cement. 

The  dolomites,  or  magnesian  limestones,  when  burned 
properly  and  reduced  to  a  powder,  will  give  a  mortar  with 
hydraulic  properties ;  and  in  general  any  magnesian  lime- 
stone containing  as  high  as  60  per  cent,  of  carbonate  of  mag- 
nesia, if  properly  burned,  will  yield  an  hydraulic  cement, 
whether  clay  be  present  or  not. 


Scott's  Hydraulic  Cement. 

116.  This  is  a  cement  invented  by  Major  Scott,  of  the 
Royal  Engineers,  British  Army,  and  is  referred  to,  not  for 
any  marked  advantages  it  possesses,  but  for  the  peculiarity 
of  its  mode  of  manufacture. 

The  limestone  is  calcined  in  the  usual  manner,  producing 
common  lime.  It  is  then,  in  layers  of  one  and  a  half  to  two 


56  CIVIL  ENGINEERING. 

feet  thick,  laid  over  the  arches  of  a  perforated  oven,  and 
brought  to  a  dull  glow.  The  fire  is  then  raked  out,  and  iron 
pots "  containing  coarse,  unpurified  sulphur  (about  fifteer 
pounds  to  each  cubic  yard  of  lime)  are  pushed  in  on  the 
grate-bars,  and  the  sulphur  ignited.  The  oven  is  closed,  sc 
as  to  prevent  the  escape  of  the  sulphurous  vapor.  After  the 
sulphur  has  been  consumed,  the  mass  is  allowed  to  cool,  anc 
is  then  ground  to  a  powder  like  other  cements. 

Why  lime  treated  in  this  manner  should  acquire  hydraulic 
properties  is  not  fully  known. 


TESTS   FOB   LIMES   AND    CEMENTS. 

117.  The  manufacture  of  limes  and  cements  having  become 
a  special  branch  of  industry  in  the  United  States  and  Europe, 
the  engineer  can  easily  obtain  the  kinds  required  for  his  pur- 
poses, and  will  rarely,  if  ever,  be  placed  in  a  position  requir- 
ing him  to  make  them.  He  will  be  more  particularly  con- 
cerned in  knowing  how  to  test  the  samples  f  '  nished  him,  so 
as  to  be  able  to  make  a  judicious  selection. 

Test  for  Rosendale  Cement. — Kosendale  cement  should 
be  ground  fine  enough  so  that  90  per  cent,  of  it  can  pass  a  No.  30 
wire  sieve  of  thirty-six  wires  to  the  lineal  inch  both  ways ; 
should  weigh  not  less  than  sixty-eight  pounds  to  the  struck 
bushel,  loosely  measured ;  and  when  made  into  a  stiff  paste 
without  sand,  and  formed  into  bars,  should,  when  seven  days 
old,  sustain,  without  rupture,  a  tensile  strain  of  sixty  pounds 
to  the  square  inch  of  cross-section,  the  sample  having  been  six 
days  in  water. 

Test  for  Portland  Cement. — Portland  cement  should  pos- 
sess the  same  degree  of  fineness  as  just  given  ;  should  weigh 
one  hundred  and  six  pounds  to  the  struck  bushel, loosely  meas- 
ured ;  and  under  the  same  conditions  should  sustain  a  tensile 
strain  of  one  hundred  and  seventy-eight  pounds  to  the  square 
inch  of  cross-section. 

Test  for  other  varieties. — The  relative  value  of  other 
varieties  of  cements  can  be  determined  by  subjecting  them 
to  similar  tests  and  comparing  the  results. 

Wire  Test. — The  wire  test  was  formerly  used  to  determine 
the  hydraulic  activity  of  samples.  It  is  as  follows :  The  paste 
is  made  into  cakes  of  one  and  a  quarter  inches  in  diameter 
and  five-eighths  of  an  inch  thick,  and  is  immersed  in  water  of 
an  established  temperature  (65°  F.) ;  the  times  are  then  noted 
which  are  required  before  the  cakes  will  support,  without  do- 


MOBTAB.  57 

prcssion,  the  point  of  a  wire  one-twelfth  of  an  inch  in  diameter 
load^xi  to  weigh  one-quarter  of  a  pound,  and  of  another  wire 
one- twenty-fourth  of  an  inch  in  diameter  weighing  one 
pound.  This  test  is  still  used  to  some  extent,  especially  by 
the  French. 

The  wire  test,  when  applied  to  cement  pastes  without  sand, 
does  not  give  a  correct  indication  of  the  values  of  their  hy. 
draulic  properties. 

STORAGE  OF  1JMES  AND  CEMENTS. 

118.  Hydraulic  limes  and  cements  deteriorate  by  exposure 
to  the  air.  If  liable  to  be  kept  on  hand  for  several  months, 
they  should  be  stored  in  a  tight  building  free  from  draught* 
of  air,  and  the  casks  should  be  raised  several  inches  above  the 
floor,  if  stone  or  earthen. 

Cements,  that  have  been  injured  by  age  or  exposure,  may 
have  their  original  energy  restored  by  recalcination.  Samples 
have  been  restored  by  being  submitted  to  a  red  heat  of  one 
hour's  duration. 

Common  lime,  for  the  same  reasons,  should  be  preserved  in 
tight  vessels.  It  is  usually  sent  to  market  in  barrels,  and  is  re- 
duced to  powder  by  slaking.  The  fineness  of  the  powder,  its 
growth,  the  phenomena  of  slaking,  and  the  degree  of  unc- 
tuousness  of  the  paste  made  with  water,  are  the  tests  for  good 
lime. 


MORTAR. 

119.  Calcareous  Mortar,  ready  for  use,  is  a  mixture,  in  a 
plastic  condition,  of  lime,  sand,  and  water.  It  is  used  to  bind 
together  the  solid  materials  in  masonry  constructions,  and  to 
form  coatings  for  the  exterior  surfaces  of  the  walls  and  inte- 
rior of  buildings. 

It  may  be  divided  into  two  principal  classes — common 
mortar  when  made  of  common  lime,  and  hydraulic  mortar 
when  hydraulic  lime  or  cement  is  used. 

When  mortar  is  thin-tempered  or  in  a  fluid  state,  it  is 
known  as  grout. 

Hardened  Mortar  is  simply  an  artificial  stone,  and  should 
fulfil  the  essential  conditions  already  given  for  stone — viz., 
should  possess  strength,  hardness,  and  durability.  These 
qualities  vary  with  the  quality  of  the  lime  or  cement 
employed,  the  kind  and  quantity  of  sand,  the  method  and 


58  CIVIL  ENGINEERING. 

degree  of  manipulation,  and  the  position,  with  respect  to 
moisture  or  dryness,  in  which  the  mortar  is  subsequently 
placed. 

Common  mortar  will  harden  only  partially  in  damp  places 
excluded  from  free  circulation  of  air,  and  not  at  all  under 
water.  These  places  are,  on  the  contrary,  favorable  to  the  in- 
duration of  hydraulic  mortars. 


Slaked  Lime. 

120.  Before  the  lime  is  mixed  with  sand  to  form  mortar,  it 
must  first  be  slaked. 

The  methods  of  slaking  lime  are  classed  under  three  heads : 
1,  drowning ;  2,  immersion;  and  3,  spontaneous  or  air  slak- 
ing. 

The  first  is  to  throw  on  the  lumps  of  lime,  just  as  they 
come  from  the  kiln,  enough  water  to  reduce  them  to  paste. 
The  workmen  are  apt  to  throw  on  more  water  than  is  required; 
hence  the  name. 

The  second  is  to  break  the  lumps  of  lime  into  pieces  not 
exceeding  an  inch  through,  then  to  place  them  in  a  basket  or 
other  contrivance,  and  to  immerse  them  in  water  for  a  few 
seconds,  withdrawing  them  before  the  commencement  of  ebul- 
lition. A  modification  of  this  method  is  to  form  heaps  of  the 
proper  size  of  these  broken  lumps,  and  then  to  sprinkle  a  cer- 
tain quantity  of  water  upon  the  lime,  the  amount  of  water 
being  from  one-fourth  to  one-third  the  volume  of  the  lime,  the 
rose  of  a  watering-pot  being  used  in  sprinkling. 

The  third  is  to  allow  the  lime  to  slake  spontaneously  by 
absorbing  moisture  from  the  surrounding  atmosphere. 

The  first  method  is  the  one  most  generally  used  in  the 
United  States. 

The  lumps  of  lime  are  collected  together  in  a  layer  from 
six  to  eight  inches  deep,  in  a  water-tight  box,  or  a  basin  of 
sand  coated  over  with  lime-paste  to  make  it  hold  water,  and 
then  the  amount  of  water  sufficient  to  reduce  the  lime  to  a 
paste  is  poured  over  them.  This  amount  of  water  is  approxi- 
mately determined  by  a  trial  of  a  small  quantity  of  lime  be- 
forehand. It  is  important  that  all  the  water  necessary  should 
be  added  at  the  beginning.  After  an  interval  of  five  or  ten  min- 
utes the  water  becomes  heated  to  the  boiling-point,  and  all 
the  phenomena  of  slaking  follow. 

^  The  workmen  are  apt  to  use  too  much  water  in  the  begin- 
ning, or,  not  using  enough,  to  add  more  when  the  slaking  if 


MORTAK.  59 

in  progress.  In  the  first  case  the  resulting  paste  will  be  too 
thin,  and  in  the  latter  the  checking  of  the  slaking  will  make 
the  product  lumpy. 

As  soon  as  the  water  is  poured  on  the  lime,  it  is  recommend- 
ed to  cover  the  mass  with  canvas  or  boards,  or  with  a  layer  of 
sand  of  uniform  thickness  after  the  slaking  is  well  under  way. 
Another  recommendation  is,  that  the  lime  be  not  stirred  while 
slaking. 

Writers  disagree  as  to  the  relative  values  of  these  three  meth- 
ods of  slaking  lime.  Supposing  that  in  the  first  process  att 
the  water  required  to  produce  a  stiff 'paste,  and  no  more  than 
this,  is  poured  on  at  the  beginning,  these  modes  may  be  ar- 
ranged in  their  order  of  superiority,  as  follows : 

For  fat  limes :  1,  drowning,  or  the  ordinary  method ;  2, 
spontaneous  slaking ;  and,  3,  immersion.  For  hydraulic  limes  : 
1,  ordinary  method;  2,  immersion;  and,  3,  spontaneous 
slaking. 

In  the  matter  of  cost,  the  first  mode  has  a  decided  advan- 
tage over  the  others.  The  second  is  not  only  expensive  from 
the  labor  required,  but  difficult  from  the  uncertainty  of  the 
period  of  immersion  at  the  hands  of  the  workmen.  The 
third  involves  the  expense  of  storage-rooms  or  sheds  and  time, 
a  period  from  twenty  days  to  even  a  year  being  necessary  to 
complete  the  slaking. 


Preservation  of  the  Lime  after  lemg 

121.  The  paste  obtained  by  the  first  mode  may  be  pre- 
served any  length  of  time  ir  kept  from  contact  with  the 
air.  It  is  usual  to  put  it  in  tig;ht  casks,  or  in  reservoirs ;  to 
put  it  in  trenches  and  cover  it  with  sand  will  be  sufficient  for 
its  preservation. 

The  powder,  from  the  second  and  third  modes,  may  be  pre- 
served for  some  time,  by  placing  it  in  casks  or  bins  with  cov- 
ers, or  in  dry  sheds  in  heaps,  covered  over  with  cloth  or  dry 
sand. 

General  Treussart  thought  that  lime  should  be  used  imme- 
diately after  it  was  slaked.  In  this  country  such  is  the  ordi- 
nary practice.  The  general  opinion  of  engineers  is  however 
adverse  to  this  practice,  and  in  some  parts  of  Europe  it  is 
the  custom  to  slake  the  lime  the  season  before  it  is  used. 


60  CTVTL  ENGINEERING. 


Sand. 

122.  Sand  is  the  granular  product  arising  from  the  disinte* 
gration  of  rocks.  It  may  therefore,  like  the  rocks  from  which 
it  is  derived,  be  divided  into  three  principal  varieties — the 
silicious,  the  calcareous,  and  the  argillaceous. 

Sand  is  sometimes  named  from  the  locality  where  it  is  ob- 
tained, as  pit-sand,  which  is  procured  from  excavations  in  in- 
land deposits  of  disintegrated  rock ;  sea-sand  and  river-sand, 
which  are  taken  from  the  shores  of  the  sea  or  rivers. 

Builders  again  classify  sand  according  to  the  size  of  the 
grain.  The  term  coarse  sand  is  applied  when  the  grain  va- 
ries between  -J  and  ^  of  an  inch  in  diameter ;  the  term  fine 
sand,  when  the  grain  is  between  -^  and  -^  of  an  inch  in  di- 
ameter ;  and  the  term  mixed  sand  is  used  for  any  mixture 
of  the  two  preceding  kinds. 

The  usual  mode  of  determining  the  size  of  sand  is  to  screen 
it  by  passing  it  through  sieves  of  various  degrees  of  fineness. 
The  sieves  are  numbered  according  to  the  number  of  open- 
ings in  a  square  inch  of  the  wire  gauze  of  which  they  are 
made. 

The  silicious  sands,  arising  from  the  quartzose  rocks,  are  the 
most  abundant,  and  are  usually  preferred  by  builders.  The 
calcareous  sands,  from  hard  calcareous  rocks,  are  more  rare, 
but  form  a  good  ingredient  for  mortar.  Some  of  the  argilla- 
ceous sands  are  valuable,  as  when  mixed  with  common  jime 
they  impart  to  it  hydraulic  properties. 

The  property,  which  some  argillaceous  sands  possess,  of 
forming  with  common  or  slightly  hydraulic  lime  a  compound 
which  will  harden  under  water,  has  long  been  known  in  France, 
where  these  sands  are  termed  arenes.  The  sands  of  this  na- 
ture are  usually  found  in  hillocks  along  river  valleys.  These 
hillocks  sometimes  rest  on  calcareous  rocks  or  argillaceous 
tufas,  and  are  frequently  formed  of  alternate  beds  of  sand 
and  pebbles.  The  sand  is  of  various  colors,  such  as  yellow, 
red.  and  green,  and  seems  to  have  been  formed  from  the  dis- 
integration of  clay  in  a  more  or  less  indurated  state.  They 
form,  with  common  lime,  an  excellent  mortar  for  masonry, 
exposed  either  to  the  open  air  or  humid  localities,  as  the  foun- 
dations of  edifices. 

Pit-sand  has  a  rougher  and  more  angular  grain  than  river 
or  sea  sand,  and  on  this  account  is  generally  preferred  by 
builders  for  mortar  to  be  used  in  brick  or  stone  work. 

River  and  sea  sand  are  by  some  preferred  for  plastoring, 


MOETAR.  61 

because  they  are  whiter  and  have  a  finer  and  more  uniform 
grain  than  pit-sand. 

The  sand  used  in  common  mortar  should  be  clean,  sharp, 
and  neither  too  coarse  nor  too  fine. 

Its  cleanliness  may  be  known  by  its  not  soiling  the  fingers 
when  rubbed  between  them  ;  and  its  sharpness  can  be  told  by 
filling  the  hand  and  closing  it  firmly,  listening  to  the  sounds 
made  by  the  particles  when  rubbed  against  each  other. 

Dirty  sand,  as  well  as  sea  sand,  should  before  using  be 
washed,  to  free  it  from  impurities. 

Sand  enters  mortar  as  a  mechanical  mixture,  and  is  used  to 
save  expense  by  lessening  the  quantity  of  lime,  to  increase 
the  resistance  of  the  mortar  to  crushing,  and  to  lessen  the 
amount  of  shrinking  during  the  drying  of  the  mortar. 

It  injures  the  tenacity  of  mortar,  and  if  too  much  be  used 
the  mortar  will  crumble  when  dry. 


PROPORTIONS  OF   INGREDIENTS. 

123.  The  quantity  or  proportion  of  sand  to  the  lime  varies 
with  the  quality  of  the  lime  and  the  uses  to  be  made  of  the 
mortar. 

Vicat  gives  for  common  mortar  the  proportion  of  2.4  parts 
of  cand  to  one  of  pure  slaked  lime  in  paste,  by  measure. 

The  practice  of  the  United  States  Corps  of  Engineers  in 
making  hydraulic  mortars  has  been  to  add  from  2.5  to  3.5  in 
bulk  of  compact  sand  to  one  of  lime  and  cement,  or  cement 
alone,  in  thick  paste. 


THE  METHOD  AND  DEGREE  OF  MANDPULATION. 

124.  The  ingredients  of  mortar  are  incorporated  either  by 
manual  labor  or  by  machinery  ;  the  latter  method  gives  re- 
sults superior  to  the  former.  The  machines  used  for  mixing 
mortar  are  the  ordinary  pug-mill  (Fig.  7),  like  those  employed 
by  brickmakers  for  tempering  clay,  the  grinding-mill  (Fig.  8), 
or  mill  of  any  other  pattern  suitable  for  the  work.  The  grind- 
ing-mill is  a  better  machine  for  this  purpose  than  the  pug-mill, 
because  it  not  only  reduces  the  lumps  found  in  the  most  care- 
fully-burnt stone  after  the  slaking  is  apparently  complete,  but 
it  brings  the  lime  to  the  state  of  a  uniform  stiff  paste,  in 
which  condition  it  should  be  before  the  sand  is  incorporated 
with  it. 


CIVIL   ENGINEERING. 


Fig.  7  represents  a  vertical 
section  through  the  axis  of  a  pug- 
mill  for  mixing  or  tempering 
mortar.  This  mill  consists  of  a 
hooped  vessel  of  the  form  of  a 
conical  frustum,  which  receives 
the  ingredients,  and  of  a  vertical 
shaft,  to  which  arms  with  teeth 
resembling  an  ordinary  rake,  are 
attached  for  the  purpose  of  mix- 
ing the  ingredients. 

A,  A,  section  of  sides  of   the 
vessel. 

B,  vertical  shaft,  to  which  the 
arms  C  are  affixed. 

D,  horizontal  bar  for  giving  a 
circular  motion  to  the  shaft  B. 


FIG.  7. 

E,  sills  of  timber  supporting  the  mill. 

F,  wrought-iron  support,  through  which  the  upper  part  of 
the  shaft  passes. 

Fig.  8  represents  a  part  of  a  mortar  mill  for  crashing 
lime  and  tempering  mortar. 


A,  a  heavy  wheel  of  timber  or 
cast  iron. 

B,  a  horizontal   bar   passing 
through   the   wheel,   fixed    to  a 
vertical   shaft,  and  arranged  at 
the    other     end,   C,    with     the 
proper  gearing  for  a  horse. 

D,  a  circular  trough  which 
receives  the  ingredients  to  be 
mixed.  The  trough  is  of  trape- 
zoidal cross-section,  from  20  to 


FIG.  8. 


30  feet  in  diameter,  about  18  inches  wide  at  top,  12  inches 
deep,  and  is  built  of  hard  brick,  stone,  or  timber  laid  on  a  firm 
foundation. 

A  good  example  of  a  grinding-mill  is  given  on  page  98  of 
Lieut.  W.  H.  Wright's  "  Treatise  on  Mortars,"  in  describing 
the  mill  used  at  Fort  Warren,  Boston  Harbor. 

The  steam  mortar-mill,  in  which  the  wheels  or  stones 
revolved  on  edge,  and  which  was  used  at  Fort  Taylor,  Key 
West,  Florida,  the  mortar  mill  of  Greyveldinger,  used  in 
Paris,  in  which  a  revolving  screw  performs  the  mixing,  as 
also  the  Fort  Warren  mortar-mill  above  alluded  to,  are  de- 


MORTAR.  63 

scribed  in  Gillmore's  "Treatise  on  Limes,  Cements,  and 
Mortars." 

125.  Process  of  making  Mortar  with  the  MilL —  The 

lime -paste  is  first  put  in  the  circular  trough,  and  to  this  is 
added  by  measurement  about  one-half  of  the  sand  required 
for  the  batch.  The  mill  is  set  in  motion,  and  the  ingredi- 
ents thoroughly  incorporated.  The  remainder  of  the  sand  is 
then  added,  and  as  much  water  as  may  be  necessary  to  bring 
the  mass  to  the  proper  consistency. 

If  common  mortar  is  to  be  rendered  hydraulic  by  adding 
hydraulic  cement,  the  latter  should  be  added  to  the  lime-paste 
just  before  the  mill  is  set  in  motion ;  a  very  quick-setting 
cement  should  not  be  added  until  the  last  portions  of  sand  are 
thrown  in. 

126.  Process  by  Hand.  —  The  measure  of  sand  required 
for  the  batch  is  placed  on  the  floor  and  formed  into  a  basin, 
in  which  the  unslaked  lime  is  placed,  the  lumps  being  broken 
to  the  proper  size.   The  necessary  quantity  of  water  is  poured 
on  by  a  hose,  watering-pots,  or  ordinary  buckets,  and  the  lime 
stirred  as  long  as  vapor  is  evolved.    The  ingredients  are  well 
mixed  together  with  the  shovel  and  hoe,  a  little  water  being 
added  occasionally  if  the  mass  be  too  stiff.     It  is  customary 
then  to  heap  the  mortar  compactly  together,  and  allow  it  tl 
remain  until  ready  for  use. 

The  rule  in  mixing  mortar,  either  by  machinery  or  hand, 
is  to  see  that  the  lime  and  sand  be  thoroughly  incorporated. 


SETTING   OF  MORTARS. 

127.  A  mortar  has  set  when  it  has  become  so  hard  that  its 
form  cannot  be  altered  without  fracture.  The  set  is  deter- 
mined by  the  wire  test.  If  the  mortar  supports  the  point  of 
the  wire  without  depression  or  penetration,  it  is  assumed  that 
the  mortar  has  set. 

Theory  of  Setting  of  Mortars. 

138.  Common  mortar  slowly  hardens  in  the  air,  from  the 
surface  towards  the  interior,  by  drying  and  by  the  absorption 
uf  carbonic  acid.  The  process  is  slow,  but  in  time,  under 
favorable  circumstances,  a  hard  material  is  produced.  The 
carbonic  acid,  absorbed  by  the  mortar,  combines  with  the 
lirne,  forming  a  carbonate  with  an  excess  of  base,  and  the 
hardening  is  due  to  this  reaction  and  to  pressure. 


64  CIVIL  ENGINEERING. 

Hydraulic  mortars,  and  paste  made  with  hydraulic  cement, 
harden  by  a  species  of  crystallization  that  takes  place  when 
the  silicates  of  lime,  alumina  and  magnesia,  which  are  anhy- 
drous after  calcination,  become  hydrates  upon  being  mixed 
with  water. 

The  compounds  which  are  formed  by  burning  the  lime- 
stone fit  to  produce  Portland  cement  at  a  high  heat  require 
but  three  equivalents  of  water  for  their  hydratiori,  while  those 
formed  at  a  low  heat  take  six.  This  is  probably  the  cause  of 
the  superior  strength  and  hardness  attained  by  the  Portland 
cement. 

In  the  cements  obtained  from  the  argillo-magnesian  lime- 
stones the  presence  of  the  silicate  of  magnesia  is  given  as  the 
reason  why  these  cements  are  more  durable  for  constructions 
in  the  sea,  as  the  silicate  of  magnesia  resists  the  action  of  sea- 
water  better  than  the  silicates  of  lime  and  alumina,  unless 
other  ingredients  introduce  adverse  conditions. 

ADHERENCE   OF  MORTAE. 

129.  The  force  with  which  mortars,  in  general,  adhere  to 
other  materials  depends  on  the  nature  of  the  material,  its 
texture,  and  the  state  of  the  surface  to  which  the  mortar  is 
applied. 

In  applying  mortars,  the  materials  to  be  joined  should  be 
thoroughly  moistened  —  a  point  too  often  neglected  —  and 
the  surfaces  made  clean.  Precautions  should  be  taken  to 
prevent  too  rapid  drying,  and  the  mortar  should  be  as  stiff  as 
it  can  be  used,  still  being  in  a  plastic  condition. 

Mortar  adheres  more  strongly  to  brick,  and  more  feebly  to 
wood,  than  to  any  other  material.  Among  stones  of  the  same 
class  it  generally  adheres  better  to  the  porous  and  coarse- 
grained than  to  the  compact  and  fine-grained.  Among  sur- 
faces it  adheres  more  strongly  to  the  rough  than  to  the 
smooth. 

The  adhesion  of  common  mortar  to  brick  and  stone,  for  the 
first  few  years,  is  greater  than  the  cohesion  of  its  own  par- 
ticles. The  contrary  is  the  case  with  hydraulic  cement. 

From  experiments  made  by  Kondelet  on  the  adhesion  of 
common  mortar  to  stone,  it  appears  that  it  required  a  force 
varying  from  15  to  30  pounds  to  the  square  inch,  applied 
perpendicular  to  the  plane  of  the  joint,  to  separate  the  mortar 
and  stone  after  six  months'  union ;  whereas  only  5  pounds  to 
the  square  inch  were  required  to  separate  the  same  surfaces 
when  applied  parallel  to  the  plane  of  the  joint. 


MORTAR. 


HARDNESS.    STRENGTH.   AND   DURABILITY   OF   MORTARS. 


65 


130.  The  same  general  rules  for  determining  these  qualities 
in  stone  are  applicable  in  mortars,  and,  as  with  stone,  experi- 
ence is  the  best  test. 

The  principal  causes  of  deterioration  and  decomposition  of 
mortars  are : 

1.  Changes  of  temperature,  producing  expansions  and  con- 
tractions. 

2.  Alternations  of  freezing  and  thawing,  producing  ex- 
foliations and  disintegrations  of  the  parts  exposed  to  their 
influence. 

Common  mortars,  which  have  had  time  to  harden,  resist 
the  action  of  severe  frosts  very  well,  if  they  are  made  rather 
poor,  or  with  an  excess  of  sand.  The  proportions  should 
be  2^-  volumes,  or  over,  of  sand  to  one  of  the  lime  in  paste. 

Hydraulic  mortars  set  equally  well  in  damp  situations  and 
in  the  open  air ;  and  those  which  have  hardened  in  the  air 
will  retain  their  hardness  if  afterwards  immersed  in  water. 
They  also  resist  well  the  action  of  frost,  if  they  have  had  time 
to  set  before  exposure  to  it ;  but,  like  common  mortars,  they 
require  to  be  made  with  an  excess  of  sand  to  withstand  well 
atmospheric  changes. 

To  ascertain  the  strength  and  compare  the  qualities  of 
different  mortars,  experiments  have  been  made  upon  the 
resistance  offered  by  them  to  cross-strains. 

The  usual  method  has  been  to  place  small  rectangular 
prisms  of  mortar,  upon  points  of  support  at  their  extremities, 
and  subject  them  to  a  cross-strain  by  applying  a  pressure  at 
a  point  midway  between  the  bearings. 

131.  Experiments  made  upon  prisms  a  year  old,  which  had 
been  exposed  to  the  ordinary  changes  of  weather,  gave  the 
following  as  the  average  strength  of  mortars  per  square  inch, 
to  resist  rupture  by  a  force  of  tension  ;  the  calculations  being 
made  from  experiments  on  the  resistance  offered  to  a  trans- 
verse strain : 

Mortars  of  very  strong  hydraulic  lime ....  170  pounds. 

"  ordinary  "  u    ....  140       " 

medium  "  «    ....  100       " 

"  common  lime 40      " 

(bad  quality)....  20       " 

General  Totten,  late  Chief  of  Engineers,  U.  S.  Army,  from 
his  experiments  deduced  the  following  general  results : 
5 


66  CIVIL  ENGINEERING. 

1.  That  mortar,  of  hydraulic  cement  and  sand,  is  the  stronger 
and  harder  as  the  quantity  of  sand  is  less. 

2.  That  common  mortar  is  the  stronger  and  harder  as  the 
quantity  of  sand  is  less. 

3.  That   any   addition   of  common  lime   to  a  mortar   of 
hydraulic  cement  and  sand,  weakens  the  mortar,  but  that  a 
little  lime  may  be  added  without  any  considerable  diminution 
of  the  strength  of  the  mortar,  and  with  a  saving  of  expense. 

4.  The  strength  of   common  mortars  is  considerably  im- 
proved by  the  addition  of  an  artificial  pozzuolana,  but  more 
BO  by  the  addition  of  an  hydraulic  cement. 

5.  Fine  sand  generally  gives  a  stronger  mortar  than  coarse 
sand. 

6.  Lime  slaked  by  sprinkling  gave  better  results  than  lime 
slaked   by   drowning.      A    few   experiments   made  on    air 
slaked  lime  were  unfavorable  to  that  mode  of  slaking. 

7.  Both  hydraulic  and  common  mortar  yielded  better  re- 
sults when  made  with  a  small  quantity  of  water  than  when 
made  thin. 

8.  Mortar  made  in  the  mortar-mill  was  found  to  be  superior 
to  that  mixed  in  the  usual  way  with  a  hoe. 

9.  Fresh  water  gave  better  results  than  salt  water. 


USES   OP  MORTAR  FOR   STUCCO,  PLASTERING,   ETC. 

132.  The  term  plastering  is  ordinarily  limited  to  the  cover- 
ing of  interior  walls  and  ceilings  by  coats  of  mortar,  while 
the  mortar  covering  exterior  walls  is  called  stucco.  This 
latter  term  was  originally  applied  to  a  species  of  plastering 
made  to  resemble  marble,  being  quite  hard  and  capable  of 
receiving  a  polish.  Outside  plastering  is  used  often  to  pre- 
vent the  rain  from  penetrating  the  joints  of  the  masonry,  and 
in  general  when  it  is  desired  to  have  a  smooth  surface  instead 
of  a  rough  one. 

Both  inside  and  outside  plastering,  when  properly  done, 
require  three  coats  to  be  used,  the  first  known  as  the  scratch 
coat,  the  second  as  the  brown,  and  the  third  as  hard  finish, 
or  stucco.  The  first  coat  is  common-lime  mortar,  with  a  given 
quantity  of  bullock's  hair  mixed  with  it.  It  contains  ordi- 
narily a  larger  proportion  of  sand  than  common  mortar  does,  so 
as  to  reduce  the  shrinkage  to  a  minimum.  When  completed 
and  partially  dry,  and  still  soft,  it  is  with  a  pointed  stick 
scratched  in  parallel  scorings  running  diagonally  acrcss  the 
surface  at  right  angles  to  each  other.  When  the  first  coat  is 


MASTIC.  67 

dry  enough,  the  brown  coat  is,  applied.  This  differs  from  the 
first  in  containing  less  hair  in  the  mixture.  This  is  followed 
by  the  third  coat,  which  is  hard  finish  for  the  inside,  or 
stucco  for  the  outside.  The  former  is  a  paste  of  fine  lime 
and  plaster  of  Paris ;  the  latter  is  a  paste  of  fine  lime  made 
stiff  with  white  sand. 

If  the  outer  plastering  is  to  be  exposed  to  the  weather,  it 
should  be  made  of  hydraulic  mortar. 

MASTICS. 

133.  Mastic  is  the  term  generally  applied  to  a  mixture  of 
powdered  limestone,  or  similar  material,  with  artificial  or  nat- 
ural combinations  of  bituminous  or  resinous  substances. 

It  is  used  as  a  cement  for  other  materials,  or  as  a  coating 
to  render  them  water-proof. 

The  term  asphalt  is  sometimes  employed  to  designate  the 
bituminous  limestone,  more  generally  the  mastic  after 'it  has 
been  moulded  into  blocks  for  transportation,  frequently  to 
the  product  obtained  by  mixing  sand  with  the  mastic,  and  by 
some  to  the  raw  bitumen  or  mineral  tar.  Callicg  the  first 
asphalt,  the  second  would  be  asphaltic  mastic,  the  third 
asphalbic  concrete,  and  the  fourth  asphaltum. 

Bituminous  Mastic. 

134.  Bituminous  mastic  is  prepared  by  heating  the  min- 
eral pitch  or  asphaltum  in  a  large  caldron  or  iron  pot,  and 
stirring  in  the  proper  proportion  of  the  powdered  limestone. 
This  operation,  although  very  simple   in  its  kind,  requires 
great   attention   and  skill  on  the  part  of   the   workmen   in 
managing  the  fire,  as  the  mastic  may  be  injured  by  too  low 
or  too  high  a  degree  of  heat.     The  best  plan  appears  to  be  to 
apply  a  brisk  fire  until  the  boiling  liquid  commences  to  give 
out  a  thin,  whitish  vapor.     The  fire  is  then  moderated  and 
kept  at  a  uniform  state,  and  the  powdered  stone  is  gradually 
added,  and  mixed  in  with  the  tar  by  stirring  the  two  well 
together.     If  the  temperature  should  be  raised  too  high,  the 
heated  mass  gives  out  a  yellowish  or  brownish  vapor.     In  this 
state  it  should  be  stirred  rapidly,  and  be  removed  at  once 
from  the  fire. 

When  the  mixing  is  completed,  the  liquid  mass  is  run  into 
moulds,  where  it  hardens  into  blocks  of  convenient  shape  and 
size. 


68  CIVTL   ENGINEERING. 

The  stone  above  used  is  a  carbonate  of  lime  naturally  im- 
pregnated with  bitumen,  called  sometimes  Seyssel  asphalt, 
from  the  place  where  it  was  quarried.  The  proportion  of 
bitumen  in  the  Seyssel  stone  is  oftentimes  as  much  as  17  per 
cent.,  and  the  amalgamation  is  more  perfect  than  that  of  any 
artificial  compound  of  the  kind  yet  invented.  To  prepare  it 
for  the  operation  just  described,  the  stone  may  be  reduced  to 
powder,  either  by  roasting  it  in  vessels  over  a  fire,  or  by  grind- 
ing it  down  in  the  ordinary  mortar-mill.  To  be  roasted,  the 
stone  is  first  reduced  to  fragments  the  size  of  an  egg.  These 
fragments  are  put  into  an  iron  vessel,  heat  is  applied,  and  the 
stone  is  reduced  to  powder  by  stirring  it  and  breaking  it  up 
with  an  iron  instrument.  This  process  is  not  only  less  eco- 
nomical than  grinding,  but  the  material  loses  a  portion  of  the 
bitumen  from  evaporation,  besides  being  liable  to  injury  from 
too  great  a  degree  of  heat.  If  to  be  ground,  the  stone  is  first 
broken  as  for  roasting.  Care  should  be  taken,  during  the 
process,  to  stir  the  mass  frequently,  otherwise  it  may  cake. 

To  use  the  mastic,  the  blocks  are  remelted,  and  the  mixture, 
in  this  state  or  mixed  with  sand,  is  laid  on  the  surface  to  be 
coated  by  pouring  it  on,  generally  in  squares,  care  being  taken 
to  form  a  perfect  union  between  edges,  and  to  rub  the  sur- 
face smooth  with  an  ordinary  wooden  float,  especially  if  an- 
other layer  is  to  be  laid  over  the  first. 

135.  Proportions. — The  proportions  for  bituminous  mastic 
are  about  1  part  of  asphaltum  to  7  or  8  by  measure  of  the 
powdered  limestone,  according  as  the  stone  contains  more  or 
less  bitumen. 

Any  petroleum  or  naphtha  present  in  the  stone  must  be 
removed ;  this  is  generally  done  by  distillation.  Clay  in  the 
limestone  injures  the  mastic,  and  is  oftentimes  the  cause  of 
the  cracks  seen  in  asphaltic  concrete  after  it  has  been  laid. 


Artificial  Mastics. 

136.  Artificial  Mastics  have  been  formed  by  mixing  coal- 
tar,  vegetable  tar,  pitch,  etc.,  with  powdered  limestone,  pow- 
derod  brick,  litharge,  etc.;  but  these  mixtures  are  inferior  to 
the  bituminous  mastic. 

The  impurities  and  volatile  ingredients  of  coal-tar,  mineral 
tar,  and  similar  substances,  render  them  less  durable  than 
mineral  pitch,  and  the  combinations  made  with  them  are  in- 
ferior to  those  made  with  the  latter,  as  might  be  expected. 
But,  for  certain  purposes,  the  artificial  mastics  are  extremely 


PRESERVATIVES.  GO 

useful,  as  they  are  quite  cheap  and  possess  in  a  measure  the 
advantages  of  bituminous  mastic. 


USES   OF   MASTICS. 

137.  The  combinations  of  asphaltum  were  well  known  to 
the  ancients,  and  a  cement  made  of  it  is  said  to  have  been 
employed  in  the  construction  of  the  walls  of  Babylon. 

The  principal  uses  of  mastic  at  the  present  day  are  for 
paving  streets,  sidewalks,  floors,  cellars,  etc.,  and  for  forming 
water-tight  coatings  for  cisterns,  cappings  of  arches,  terraces, 
and  other  similar  roofings. 

It  has  quite  an  extensive  use  in  Europe  at  the  present  time. 
The  principal  sources  of  the  asphalt  are  the  Jurassic  range  in 
the  Yal  de  Travers,  Pyrimont,  Seyssel  on  the  Rhone,  and  the 
neighboring  localities,  and  Bechelbronn  (or  Lobsan),  in  Alsace. 

Asphaltum  alone  has  been  frequently  used  for  coatings,  but 
in  time  it  becomes  dry  and  peels  off.  But  made  into  mastic, 
evaporation  is  prevented  and  its  durability  increased. 

The  use  of  the  mastic,  for  making  asphaltic  concrete,  has 
already  been  described. 


CHAPTER  V. 
PRESERVATIVES. 

PAINTS. 

138.  Paints  are  mixtures  of  fixed  and  volatile  oils,  chiefly 
those  of  linseed  and  turpentine,  with  certain  of  the  metallic 
salts  and  oxides,  and  with  other  substances ;  the  latter  are  used 
either  as  pigments  or  stainers,  or  to  give  what  is  termed  a  body 
to  the  paint,  and  also  to  improve  its  drying  properties. 

Paints  are  mainly  used,  as  protective  agents,  to  secure  wood 
and  metals  from  the  destructive  action  of  air  and  water.  As 
they  possess  only  a  limited  degree  of  durability,  they  must  be 
renewed  from  time  to  time.  They  are  more  durable  in  air 
than  in  water. 

The  principal  materials  used  in  painting  are:    Red  and 


70  CTVTL  ENGINEERING. 

•white  lead,  red  and  yellow  ochre,  prussian  blue,  verdi- 
gris, lamp-black,  litharge,  linseed-oil,  and  spirits  of  tur- 
pentine. 

By  suitably  combining  the  above,  almost  any  color  may  be 
obtained.  For  example,  a  lead  color  is  obtained  by  mixing  a 
little  lamp-black  with  the  white  lead,  etc. 

Linseed-oil,  being  boiled  with  the  addition  of  a  small  quan- 
tity of  litharge  and  sugar-of-lead,  forms  what  is  known  as 
drying  oil. 

Spirits  of  turpentine  is  not  generally  used  in  the  paints 
intended  for  external  and  finishing  coats,  as  it  does  not  stand 
exposure  as  well  as  oil. 

139.  In  painting  wood,  the  first  thing  to  be  done  is  to  clean 
and  smooth  the  surface  to  be  covered.  If  the  wood  be  resin- 
ous the  knots  must  be  killed  before  the  paint  is  applied  ;  this 
is  done  by  applying  a  coat  of  red  lead  mixed  with  sizing. 
The  surface  being  dry,  the  first  coat,  generally  white  lead 
mixed  with  linseed  oil,  is  put  on ;  this  is  called  priming. 
This  coat  being  dry,  all  holes,  indentations,  heads  of  nails, 
etc.,  should  be  filled  and  covered  over  with  putty.  The 
second  coat  of  paint  is  then  applied.  If  it  be  old  work  that 
is  to  be  repainted,  the  entire  surface  should  be  scrubbed  with 
soap  and  water,  well  scraped,  and  then  rubbed  down  with 
sand-paper  or  pumice,  in  order  to  get  rid  of  the  old  paint 
and  to  obtain  an  even,  smooth  surface. 


JAPANNING. 

140.  Japanning  is  the  name  given  to  the  process  which 
forms  over  the  surface  of  the  material  to  be  covered,  a  hard, 
smooth,  varnish-like  coating.  [Art.  80.] 


OILING. 

141.  Oiling  is  frequently  used  as  a  preservative.  It  may 
be  done  either  while  the  surface  to  be  protected  is  hot  or  eold. 
Linseed-oil  is  the  material  generally  used. 


VARNISHES. 

142.  Varnishes  are  made  by  dissolving  resinous  substances 
til  alcohol,  or  in  linseed-oil  and  spirits  or  turpentine,  just  as 
paints  are  made  by  similarly  dissolving  or  mixing  pigments. 


PRESERVATIVES.  71 

Varnishes  are  used  for  the  same  purpose  as  paints,  but 
especially  when  it  is  desired  to  give  a  clear,  shining  appear- 
ance to  the  surface  on  which  they  are  laid. 


COAL-TAR. 


143.  Coal-tar  is  much  used  as  a  preservative.  It  may  be 
applied  as  a  coating  for  the  material,  or  it  may  be  applied  by 
the  process  known  as  "  creosoting."  [Art.  25.] 


ASPHALTUM. 


144.  Asphaltum  is  used  for  the  same  purposes.    Its  uses 
are  described  in  Art.  137. 


METAL    COVERINGS. 

145.  Plating. — Protection  is  frequently  afforded  by  cover- 
ing the  material  with  a  thin  coating  of  a  metal  which  is  not 
affected,  or  to  a  very  slight  degree,  by  the  destructive  agencies 
to  be  guarded  against. 

Zinc  applied  to  iron,  by  the  process  of  "  galvanizing,"  pro- 
tects iron  from  direct  action  of  the  air  and  moisture  as  long 
as  the  coating  is  perfect.  [Art.  82.] 

Tin  is  used  for  the  same  purpose. 

Nickel  has  been  tried  for  brass. 


OTHER  PRESERVATIVES BY   CHEMICAL   COMBINATIONS. 

146.  Salts  of  Silica  have  been  tried  for  protection  of 
building  stones.  [Art.  35.] 

Various  salts  have  been  used  to  saturate  timber,  thus 
changing  the  albuminous  substances  in  the  timber  into  insol- 
uble compounds  by  chemical  action,  and  thus  increasing  its 
durability.  [Art.  25.] 


72  CIVIL   ENGINEERING. 


PART  II. 

STRENGTH  OF  MATERIALS. 

CHAPTER  YL 
STRAINS. 

147.  The  materials  in  a  structure  are   subjected  to  the 
action  of  various  forces,  according  to  the  kind  of  construction 
of  which  they  form  a  part,  and  the  position  they  occupy  in  it. 

In  planning  a  structure,  two  general  problems  are  to  be 
considered. 

I.  The  nature  and  magnitude  of  the  forces  which  are  to 
act  on  it ;  and, 

II.  The  proper  distribution  and  size  of  its  various  parts,  so 
that  they  shall  successfully  resist  the  action  of  these  forces. 

In  the  former,  if  the  intensities,  directions,  and  points  of 
application  be  known,  the  effect  that  the  forces  will  exert 
may  be  determined. 

In  the  latter,  it  is  necessary  to  have  a  knowledge  of  the 
strength  of  the  materials  to  be  used  in  the  structure. 

148.  Strength  depends  upon  the  internal  organization  of 
a  body,  and  a  material  is  said  to  have  the  requisite  strength — 
to  be  strong  enough — when,  by  reason  of  certain  inherent 
physical  properties,  it  possesses  the  ability  to  resist  the  action 
of  an  external  force  within  limits. 

All  materials  have  not  equal  strength,  nor  does  the  same 
material  resist  equally  the  same  force,  when  a  change  is 
made  in  its  direction  or  point  of  application. 

The  degree  of  strength  that  a  material  possesses  is  deter- 
mined  by  experience  or  experiment. 

As  it  is  not  always  practicable  nor  expedient  to  submit  to 
the  test  of  an  actual  experiment  the  piece  to  be  used  in  a 
structure,  its  assumed  degree  of  strength  is  obtained  either 
by  subjecting  a  piece  of  the  same  material,  having  the  same 
dimensions,  to  conditions  similar  to  those  to  which  the  for- 
mer is  to  be  submitted ;  or  knowing  the  relations  between 


STRAINS.  73 

the  strengths  of  pieces  of  the  same  material  of  different  di- 
mensions, by  deducing  it  These  relations  are  obtained  by 
means  of  mathematics,  and  are  confirmed  by  experience. 

149.  Strains. — Every  solid  body  is  supposed  to  be 
formed  of  molecules,  infinitely  small  and  infinitely  close  to 
each  other,  grouped  together  by  certain  laws.  Each  mole- 
cule is  supposed  to  be  so  related  to  those  surrounding  it 
that  its  position  cannot  be  changed  except  by  the  application 
of  an  extraneous  force. 

If  a  solid,  which  is  not  allowed  to  move  from  its  place,  be 
acted  upon  by  an  extraneous  force  the  equilibrium  of  the  in- 
ternal forces  acting  between  the  molecules  will  be  disturbed 
and  variations  caused  in  the  distances  between  the  molecules, 
and  in  the  intensities  of  the  forces  that  bind  them  together. 

By  these  variations,  an  equilibrium  between  the  external 
and  internal  forces  is  effected,  and  an  alteration  of  the  form 
of  the  solid  is  caused.  This  alteration  of  form  is  called  a 
strain,  and  the  force  by  which  the  molecules  resist  it  is 
called  a  stress. 

Since,  for  any  section  of  a  solid,  the  force  developed  in 
the  body  at  the  section  is  equal  to  the  external  force  acting 
at  that  section  to  produce  a  strain,  the  term  stress  is  fre- 
quently applied  to  the  straining  force  acting  at  that  section. 

External  forces,  therefore,  acting  upon  solids  not  free  to 
move  cause  strains  and  develop  stresses  in  the  bodies  so 
placed. 


CLASSIFICATION  OP  STRAINS. 

150.  If  a  solid  body  like  that  of  a  beam  (Fig.  9)  be  firmly 
fastened  at  one  end  so  that  it  will  not  move,  and  then  be 
acted  upon  by  an  extraneous  force,  this  beam  will  be  sub- 
jected to  a  strain.  Stress  will  be  developed  in  the  beam  to 
resist  the  strain  and  to  establish  an  equilibrium  between  the 
external  and  internal  forces. 

When  a  beam,  or  any  solid  body,  is  strained,  the  element- 
ary particles  or  fibres  of  which  it  is  composed  will  have  their 
figures  and  dimensions  changed  by  the  action  of  the  strain- 
ing force.  If  these  particles  be  cubical  in  form  before  the 
application  of  the  external  force,  they  will,  after  the  force 
has  been  applied,  become  parallelepipeds,  either  right  or  ob- 
lique. In  considering  the  distortions  of  the  elementary  par- 
ticle, the  particle  being  assumed  to  be  infinitely  small,  the 


CIVIL   ENGINEERING. 


curvature  of  the  faces  produced  by  the  distortion  may  be 
regarded  as  inappreciable. 

To  examine  the  distortions  to  which  a  particle  of  the  beam 
is  exposed,  let  it  be  assumed  that  the  beam  is  of  a  homo- 
geneous material  and  its  axis  is  parallel  to  one  of  the  linear 
dimensions  of  the  cubical  elementary  particle.  Suppose  the 
beam  to  be  intersected  by  two  planes  perpendicular  to  its  axis 
and  infinitely  near  each  other.  Let  A  B  and  C  D  be  the  sec- 


c  c 


-f, 


PIG.  9. 


FIG.  10. 


tions  cut  from  the  beam  by  these  planes.  Suppose  the  sec- 
tion A  B  to  be  fixed  and  the  section  C  D  to  take  all  the  posi- 
tions it  can  have  with  respect  to  the  fixed  section. 

1.  Let  the  action  of  the  straining  force  be  such  that  the 
section  C  D,  while  remaining  parallel  to  A  B,  shall  move  away 
from  it.     This  can  be  done  only  by  lengthening  the  fibres 
connecting  the  two  sections;  and  since  the  sections  remain 
parallel,  by  lengthening  all  of  them  an  equal  amount. 

This  distortion  of  lengthening  the  fibres  is  called  a  strain 
of  tension,  the  resistance  offered  by  the  fibre  is  called  a 
tensile  stress,  and  the  external  force  producing  the  strain, 
a  force  of  extension. 

2.  If  the  force  acting  on  the  section  C  D  had  been  such  as 
to  make  it  approach  A  B,  but  still  be  parallel  to  it,  the  fibres 
would  have  been  shortened.     The  strain  would  have  been 
one  of  compression ;  the  stress,  compressive ;  and  the 
straining  force,  a  crushing  one. 

3.  Suppose  the  section  C  D,  under  the  action  of  the  force, 
had  taken  a  position  as  C'  D',  by  turning  around  some  line 
in  its  plane,  as  0'.    This  position  could  not  have  been  as- 
sumed unless  the  fibres  were  deflected,  and  the  fibres  above 
the  axis  of  rotation  lengthened,  and  those  below  it  short- 
ened.    The  distortion  of  the  fibre  in  this  case  is  called  a 
cross  strain ;  the  stress,  a  transverse  one ;  and  the  strain- 
ing force,  a  bending  force,  or  force  of  flexure. 


STRAINS. 


4.  Suppose  the  section  C  D,  under  the  action  of  the  force, 
to  be  moved  past  A  B,  but  the  planes  of  the  sections  kept 
parallel.     This  position  would  require  the  fibres  to  be  dis- 
torted as  shown  in  Fig.  11,  in  which  the  fibre  a  b  takes  a 
new  position  as  a  b'.     Since  the  planes 

remain  parallel,  all  the  fibres  connecting 

the  sections  are  distorted  equally.   This 

distortion  is  called  a  shearing  strain  ; 

the  stress,  a  shearing  one,  or  simply  a 

shear;    and    the    straining    force,    a  FIG.  11. 

shearing  force. 

5.  The  section  C  D  may  by  the  action  of  the  force  be  made 
to  revolve  around  some  line  perpendicular  to  its  plane.   The 
fibres  connecting  the  sections  would  become  distorted,  tak- 
ing the  form  of  oblique  parallelopipeds  with  helical  axes. 
This  distortion  is  called  a  strain  of  torsion  ;   the  stress, 
torsion  ;  and  the  straining  force,  one  of  twisting. 

The  section  C  D  can  be  made  to  take  other  positions  than 
the  ones  given,  but  on  examination  of  any  one  of  such  posi- 
tions, it  will  be  found  to  be  one  of  those  just  described,  or 
one  which  can  be  separated  into  two  or  more  of  them.  It 
follows,  therefore,  that  every  strain  of  an  elementary  fibre 
caused  by  an  extraneous  force  will  be  one  of  those  named, 
or  a  combination  of  two  or  more  of  them. 

In  considering  the  strains  of  the  elementary  particles  of  a 
body  at  a  given  section  of  the  body,  the  sum  of  all  the  stresses 
developed  in  the  fibres  at  this  section  is  the  stress  developed 
at  the  section  considered. 

151.  Examples.  —  Weights,  either  permanently  or  tem- 
porarily applied  to  a  solid,  form  the  extraneous  forces  that 
ordinarily  strain  a  structure.  The  stresses  developed  are  as 
follows  : 

1.  Compressive  ;  as  the  stress  developed  in    a  pillar 
when  a  load  is  placed  on  its  top.     The  load  tends  to  shorten 
the  fibres,  causing  a  strain  of  compression  on  the  pillar. 

2.  Tensile  ;  as  the  stress  developed  in  a  rod,  chain,  etc., 
fastened  at  one  end  and  sustaining  a  weight  at  the  other. 
The  load  tends  to  lengthen  the  fibres,  causing  a  strain  of 
tension  on  the  rod,  etc. 

3.  Transverse  ;  as  the  stress  developed  by  a  load  placed 
on  a  beam  supported  at  its  extremities.     The  action  of  the 
load  is  to  bend  the  beam  and  cause  a  cross  strain. 

4.  Shearing  ;  as  that  where  the  effect  of  the  load  is  to 
pull  apart,  in  the  direction  of  their  lengths,  two  plates  or 
bars  of  iron  that  are  held  together  by  rivets.     The  action  of 
the  force  is  such  as  to  cause  a  shearing  strain  on  the  rivets. 


76  CIVIL   ENGINEERING. 

5.  Torsion ;  as  that  developed  by  a  weight  lifted  by  a 
windlass.  The  action  of  the  force  causes  a  strain  of  torsion 
on  the  axle.  This  strain  is  common  in  machinery  but  not  in 
structures,  as  care  is  taken  to  distribute  the  loads  over  the 
latter  so  as  to  avoid  developing  a  torsional  stress  in  the  mate- 
rial. 

Each  strain  is  accompanied  by  its  corresponding  stress, 
which  is  an  increasing  function  of  the  strain.  When  the 
relation  between  a  strain  and  its  stress  is  known,  the  latter 
can  be  expressed  in  terms  of  the  strain,  equations  formed, 
and  the  strength  of  the  solid  determined. 

152.  Elasticity  is  that  property  of  a  body  by  which  the 
particles,  when  disturbed  by  an  extraneous  force,  tend  to 
return  to  their  original  positions  upon  the  extraneous  force 
ceasing  to  act. 

"When  the  displacements  of  the  particles  are  very  small, 
the  particles  upon  the  removal  of  the  disturbing  force  re- 
sume their  positions  by  the  action  of  the  elastic  force,  and 
the  strain  is  said  to  be  within  the  limit  of  elasticity. 

The  potential  energy  of  elasticity  of  a  particle  while  dis- 
torted is  the  work  which  it  is  capable  of  performing  in  re- 
turning to  its  original  position. 

Experiment  shows  that  within  the  limit  of  elasticity  the 
strains  vary  continuously,  and  are  proportional  to  the  forces 
causing  them.  The  corresponding  stresses  being  functions  of 
the  strains,  may  be  represented  by  the  strains  multiplied  by 
a  constant  quantity.  This  constant  is  called  the  coefficient 
of  elasticity. 

The  coefficient  of  elasticity  varies  both  with  the  kind  of 
material  of  which  the  solid  is  composed  and  with  the  kind  of 
strain,  being  different  when  the  strains  are  alike  and  the  ma- 
terial different,  and  different  when  the  material  is  the  same 
but  the  strains  are  unlike. 

The  general  method  used  to  obtain  the  relations  existing 
between  the  strains  of  bodies  and  the  corresponding  stresses 
is  to  suppose  the  solid  to  be  composed  of  elementary  particles, 
each  particle  being  a  volume  of  regular  geometrical  form. 
The  elementary  particle  is  then  referred  to  a  system  of  rect- 
angular co-ordinate  planes  with  its  linear  dimensions  parallel 
to  the  co-ordinate  axes,  and  supposed  to  be  subjected  to  any 
stress  whatever  within  the  limit  of  elasticity. 

The  stress  is  supposed  to  be  separated  into  its  six  element- 
ary ones — three  acting  in  the  direction  of  the  linear  dimen- 
sions of  the  particle  to  lengthen  or  to  shorten  the  particle, 
and  three  along  the  faces  to  alter  the  angles  between  the  faces 


STRAINS.  77 

of  the  particle.  The  first  three  are  known  as  normal,  and 
the  latter  three,  as  tangential  stresses. 

The  strain  caused  in  the  particle  by  the  action  of  the  stress 
is  also  divided  into  its  elementary  ones.  The  strains  affect- 
ing the  length  of  the  linear  dimensions  of  the  particle  are 
known  as  the  direct,  and  those  affecting  the  angles  between 
the  faces  as  transverse  strains. 

The  form  of  the  particle  having  been  assumed  to  be  a 
cube,  or  a  right  parallelepiped,  the  equation  of  its  surface 
referred  to  the  co-ordinate  axes  is  known.  The  displacements, 
or  elementary  strains  caused  by  the  elementary  stress  can 
be  expressed  in  terms  of  the  co-ordinates  and  the  differen- 
tials entering  the  equation  of  the  surface.  The  strains 
having  been  determined  in  extent  and  kind,  the  corre- 
sponding stresses  can  be  expressed  in  terms  of  these  strains 
and  constants.  Equations  may  then  be  formed,  which 
being  integrated  will  give  the  total  strains  and  stresses  in 
the  solid. 

Approximate  methods  are  generally  employed  to  find 
the  relations  between  the  strains  and  the  corresponding 
stresses,  and  are  considered  sufficiently  accurate  for  all 
practical  purposes.  They  will  be  employed  in  the  follow- 
ing pages. 

The  approximate  method  is  to  conceive  the  solid  to  be 
divided  by  a  plane  into  two  parts  ;  then  to  find  all  the  extrane- 
ous forces  acting  on  one  of  these  parts,  on  either  side  of  the 
plane,  to  strain  the  body ;  then  place  the  straining  forces  thus 
found  equal  to  the  entire  stress  developed  in  the  body  at  the 
section  made  by  the  plane ;  assume  the  stress  at  this  section 
to  be  distributed  according  to  some  law,  deduced  by  experi- 
ment or  theory,  which  is  assumed  to  be  true,  or  practically 
so,  as  regards  the  exact  state  of  distribution ;  form  equa- 
tions expressing  these  conditions  and  applying  to  the  particu- 
lar cases  under  consideration.  A  discussion  of  the  equations 
thus  formed  will  give  the  stress  on  the  unit  of  area  of  the 
section,  the  amount  of  strain,  and  the  strength  of  the  mate- 
rial necessary  to  resist  the  stress  acting  at  the  section. 


CONSTANTS. 

153.  In  discussing  the  equations  deduced  for  determining 
the  strength  of  building  materials,  certain  constants  are  in- 
volved which  depend  for  their  value  on  the  physical  proper- 
ties of  the  material  under  consideration.  These  constants 


78  CIVIL   ENGINEERING. 

have  been  or  are  to  be  determined  for  each  material  by 
actual  experiment. 

There  are  four  principal  ones : 

I.  The  weight,  or  specific  gravity  of  the  body ; 

II.  The  limit  of  elasticity ; 

III.  The  coefficient  of  elasticity ; 

IV.  The  modulus  of  rupture. 

154.  The  weight  enters  as  an  element  in  all  construc- 
tions; and  to  such  an  extent  in  some,  as  in  masonry  for 
example,  that  the  moving  or  temporary  loads  to  be  borne 
may  be  disregarded,  or  considered  as  insignificant,  in  com- 
parison with  the  weight  of  the  structure  itself. 

155.  Limit  of  Elasticity. — From  a  great  number  of 
experiments,  made  on  a  great  variety  of  materials,  it  has 
been  found  that  practically, 

1st.  All  bodies  are  elastic. 

2d.  Within  very  small  limits  they  may  be  considered  as 
perfectly  elastic. 

3d.  Within  the  elastic  limit  the  amount  of  displacement  is 
directly  proportional  to  the  force  that  produces  it. 

4th.  Within  a  considerable  distance  beyond  the  elastic  limit 
the  amount  of  displacement  is  not  exactly  but  nearly  propor- 
tional to  the  force  producing  it. 

The  limit  of  elasticity  of  a  body  in  any  direction  is  deter- 
mined by  experiment,  and  its  determination  is  a  matter  of 
great  nicety ;  hence  experimenters  have  paid  more  attention 
to  determining  the  ultimate  strength  of  materials ;  that  is, 
to  finding  the  limits  beyond  which  any  additional  load  will 
break  the  material. 

If  the  material  be  strained  beyond  the  elastic  limit,  the 
particles  will  not  resume  their  former  positions,  and  a  per- 
manent change  of  figure  is  the  result.  This  permanent 
change  is  called  a  set.  A  set,  when  it  is  made,  does  not 
necessarily  weaken  the  material,  but  it  is  better  in  most 
cases  not  to  have  it. 

156.  Coefficient  of  Elasticity.— The    coefficients    of 
elasticity  vary  with  the  material,  and  with  the  kind  of  stress 
developed. 

Let  it  be  required  to  determine  the  coefficient  of  elasticity 
for  a  homogeneous  material  strained  only  by  a  force  of 
extension.  Assume  the  material  to  be  in  the  form  of  a 
straight  bar  of  uniform  cross-section,  fastened  at  one  end, 
and  pulled  by  forces  whose  resultant  acts  along  the  axis  of 
the  bar.  The  intensity  of  the  pull  will  be  uniform  on  each 
cross-section. 


STRAINS.  Y9 

Let  W  =  the  total  pull,-  L  =  the  length  of  the  bar  before 
it  is  strained,  A  =  the  area  of  its  cross-section,  and  I  =  the 
elongation  of  the  bar  caused  by  the  force  W. 

W 

Then,  -r-  =  the  force  acting  on  a  unit  of  cross-section, 
A 

and  j  =  the  amount  of  elongation  for  a  unit  of  length  of 

the  bar. 

Since  the  pull  is  uniformly  distributed  over  the  cross-sec- 
tion. it  is  assumed  that  the  stress  developed  in  the  cross-sec- 

w 

tion  is  so  distributed,  and  that  —  =  the  intensity  of  the 

.A. 

stress  on  any  unit  of  cross-section  of  the  bar.  But,  the  stress 
is  equal  to  the  strain  multiplied  by  a  constant,  hence  we 
have 

W      I 


in  which  E  is  the  coefficient  of  elasticity.     "Whence, 


By  means  of  formula  (1)  the  coefficient  of  elasticity 

for  a  homogeneous  material  strained  by  a  force  of  extension 
can  be  obtained  by  experiment. 

The  following  are  some  of  the  values  of  E,  that  have  been 
obtained  by  experiment  for  various  building  materials,  viz.  : 

Material.  Value  of  E. 

Cast  Iron  ......................  18,400,000  Ibs. 

Wrought  Iron  ..................  24,000,000  " 

Lead  (cast)  .....................        720,000   " 

Steel  ..........................  29,000,000  " 

Tin  (cast)  .....................     4,608,000  " 

Zinc  (cast)  ......................  13,680,000   " 

Ash  ...........................     1,644,800  " 

Fir  ...........................     1,191,200   « 

Pine,  pitch  .....................     1,225,600   " 

"     yellow  ....................     1,600,000   " 

Oak  ...........................     1,451,200  " 

Marble  ........................     2,520,000   " 

Limestone  (common)  ............     1,533,000   " 

157.  Modulus  of  Rupture.  —  If  the  straining  forces  be 
continually  increased  in  intensity,  they  will  produce  in  time 


80  CIVIL   ENGINEERING. 

a  rupture,  or  such  a  disfigurement  of  the  solid  as  to  make 
the  material  unfit  for  building  purposes. 

At  the  moment  of  rupture,  or  an  instant  before,  the  inten- 
sity of  the  stress  developed  in  the  material  is  greater  than  at 
any  other  period  of  the  strain.  This  greatest  intensity  of 
the  stress  is  known  as  the  "  ultimate  resistance  "  of  the 
material,  and  its  value  is  obtained  by  experiment. 

When  the  material  is  subjected  to  a  strain  of  tension 
alone,  the  tensile  stress  is  supposed  to  be  distributed  ^ uni- 
formly over  its  cross-section,  and  the  stress  on  the  unit  of 
area  is  equal  to  the  total  stress  divided  by  the  area  of  cross- 
section.  When  this  straining  force  is  increased  sufficiently 
to  produce  rupture  of  the  material,  the  stress  on  the  unit  of 
area,  at  the  moment  rupture  begins,  is  taken  as  the  measure 
of  its  ultimate  resistance.  '  This  stress  on  the  unit,  or  the 
force  necessary  to  pull  asunder  a  piece  whose  cross-section 
is  unity  is  called  the  modulus  of  tenacity  for  that  mate- 
rial. 

If  the  stress  is  a  compressive  one,  or  a  shear,  the  corre- 
sponding stress  on  the  unit  of  section,  at  the  moment  of 
rupture,  is  called  the  modulus  of  crushing,  or  modulus 
of  shearing,  as  the  case  may  be. 

The  values  of  these  moduli  are  obtained  by  experiment, 
and  are  represented  in  the  formulas  by  the  letters  T,  C,  and 
S. 

When  the  strain  is  a  cross  one,  the  transverse  stress  de- 
veloped at  a  given  cross-section  is  not  supposed  to  be  dis- 
tributed as  just  described,  but  is  assumed  to  vary  uniformly 
over  the  cross-section,  being  greatest  on  the  units  farthest 
from  the  axis  of  rotation.  The  stress  on  the  unit  of  cross- 
section  at  the  surface  of  the  material  when  the  fibres  begin 
to  tear  apart,  or  to  crush,  is  taken  as  the  measure  of  ultimate 
resistance  to  cross  strain,  and  is  called  the  modulus  of 
rupture,  which  is  represented  in  the  formulas  by  the  letter 
R. 

It  would  seem,  since  the  rupture  of  a  piece  by  a  cross 
strain  takes  place  by  the  fibres  being  torn  apart  or  crushed, 
that  the  respective  values  of  E,  C,  and  T  for  the  same  mate- 
rial would  be  the  same,  or  at  least  nearly  equal,  and  that  one 
symbol  might  be  used  to  represent  the  respective  values  of 
the  three.  Experiment  shows,  however,  that  they  are  not 
equal,  but  vary  considerably. 

If  the  stress  is  one  of  torsion,  the  stress  on  the  unit  far- 
thest from  the  axis  is  taken  as  the  measure,  is  called  the 
modulus  of  torsion,  and  is  represented  in  the  formulas 
by  the  letters  Tt. 


TENSION. 
TENSION. 


81 


158.  Extraneous  forces  acting  on  a  piece  fastened  at  one 
end,  and  in  the  direction  of  its  axis,  produce  a  strain  of  ex- 
tension in  the  piece,  if  the  direction  of  the  resultant  is  from 
the  fixed  end,  and  of  compression  if  the  direction  is  to- 
ward it. 

Let  it  be  required  to  determine  the  elongation  pro- 
duced in  a  straight  bar,  of  uniform  cross-section,  placed 
in  a  vertical  position  and  fixed  at  one  end,  by  a  system  of 
forces  whose  resultant  acts  along  the  axis  of  the  bar. 

Represent  by  (Fig.  12) 

L,  the  original  length  of  the  bar, 

W,  the  force  applied  to  lengthen  it, 

I,  the  elongation  due  to  W, 

A,  the  area  of  the  cross-section, 

E,  the  coefficient  of  elasticity. 

Then  from  eq.  (1),  we  have 


and, 


(3) 


Eq.  (2)  shows  that  the  elongation  is 
directly  proportional  to  the  length  of 
the  bar  and  to  the  force  itself,  and  in- 
versely to  the  area  of  the  cross-section 
and  coefficient  of  elasticity ;  which  is 
fully  confirmed  by  experiment. 


FIG.  12. 


If  in  eq.  (3)  we  make  A  =  1  and  I  =  L,  we  shall  have 


That  is,  the  coefficient  of  elasticity,  E,  is  fas  force  which,  ap- 
plied to  a  bar,  the  cross-section  of  which  is  a  superficial 
unit,  would  produce  an  elongation  equal  to  the  original 
length  of  the  bar,  supposing  its  elasticity  perfect  up  to  this 
limit. 

This  is  a  theoretical  force ;  but  as  the  law  upon  which  it 

depends  is  true  within  the  limits  of  elasticity,  knowing  W,  A, 

and  L,  and  determining  I  by  measurement,  the  value  that  E 

would  have  if  the  elasticity  remained  perfect  is  easily  found. 

6 


82  CIVIL  ENGINEERING. 

Divide  W  by  A,  and  we  have 

_  =  the  stress  on  a  unit  of  cross-section. 
A 

If  W7  be  the  force  necessary  to  produce  rupture  when  act- 
ing in  the  direction  of  the  axis,  then 

—  =  T,  the  modulus  of  tenacity. ...  (5) 
A 

Wood  and  iron  are  the  two  building  materials  most  fre- 
quently exposed  to  this  strain.  The  cohesive  power  of  wood  is 
greatest  in  the  direction  of  the  fibres,  and  in  the  tables  showing 
the  results  of  the  experiments  made  on  the  strength  of  mate- 
rials, the  tensile  strength  there  given  is  taken  with  reference 
to  that  direction,  unless  otherwise  stated. 

From  eq.  (5),  we  have  W  =  TA,  from  which  knowing 
T  and  A,  the  force  necessary  to  rupture  the  bar  may  be 
deduced. 

159.  The  following  table  gives  the  tensile  strength,  per 
square  inch,  as  obtained  by  experiment  upon  some  of  the  ma- 
terials frequently  used  in  building : 

Material.  Tensile  Strength  per  sq.  inch. 

Ash 10,803  Ibs.  to  24,033  Ibs. 

Chestnut 11,891  "    "  13,066  " 

Cedar «     «  10,300  " 

Hickory 12,866  «    "  40,067  " 

Oak,  white 12,300  "    "  25,222  « 

"     live 15,800  " 

Pine 11,400  "    "19,200  « 

Fir . .  12,867  "     "  16,833  « 

Hemlock 16,533  " 

Cast  iron,  common  pig 15,000  u 

"    good  common 

iron 20,000  « 

Bar  iron 57,000  « 

"      "    Swedish 72,000  " 

Copper  wire 60,000  " 

Steel,  cast 128,000  " 

"      shear 124,000  " 

"      puddled 105,000  " 

Tin,  cast 4,800  " 

Lead,  "  1,800  " 

Zinc 


TENSION.  83 

The  specimens  of  wood  in  the  foregoing  list  were  dry  and 
seasoned.  The  time  of  seasoning  varying  from  one  to  fifteen 
years.  They  were  grown  in  different  parts  of  the  United 
States,  extending  from  the  extreme  north  to  the  farthest  south, 
and  from  the  Atlantic  coast  to  the  Pacific.  The  differences 
in  the  localities  from  whence  they  were  brought  and  the  times 
of  seasoning,  explain  the  differences  observed  in  the  tensile 
strength  of  specimens  of  the  same  wood. 

The  tensile  strength  of  the  metals  is  materially  modified  by 
the  processes  of  manufacture  and  by  the  impurities  they 
contain. 

It  is  evident,  from  this  table,  and  from  what  has  been  just 
stated,  that  it  is  not  practicable  to  assume  a  value  for  the 
modulus  of  tenacity  which  will  be  safe  and  economical  for  a 
given  material.  Its  value  in  any  particular  case  should  be 
determined  by  experiment;  or  before  its  value  can  be 
assumed,  the  quality  of  the  material  must  in  some  way  be 
known. 

The  "work  expended  in  the  elongation  of  the  bar. 
160.  The  general  formula  from  Anal.  Mechanics  is 

Q  = 


in  which  P  is  the  resistance,  s  the  path  of  the  point  of  appli- 
cation, and  Q  the  quantity  of  work. 

In  this  formula,  substitute  W  for  P,  and  I  the  elongation 
for  s,  and  we  have 


Q  = 


Substituting  for  W  its  value  from  eq.  (3),  there  obtains, 


Q  = 


to  represent  the  quantity  of  work. 

Integrating  between  the  limits  I  =  0  and  I  =  I',  we  have, 


Q  =  i        ^  = 

L 


34  CIVIL    ENGINEERING. 

From  eq.  (3)  we  have 

EA*'  -W 
~L~ 

W7  being  the  particular  value  of  W  producing  the  elonga- 

tion, I'. 

Substituting  this  value  of  W  in  the  preceding  equation, 

and  we  have 


If,  in  the  eq. 

Q  = 

W  were  constant  and  equal  to  W,  then 
Q  =  WJ*dl, 

which  integrated  between  the  limits  I  =  0  and  I  —  I'  will  give 

Q  =  WT. 

This  value  of  Q  is  twice  that  of  Q  in  eq.  (6)  ;  whence  it 
follows  that  the  work  expended  in  producing  the  elongation 
?,  by  applying  the  force  W',  at  once,  and  keeping  it  constant, 
is  twice  the  work  which  would  be  expended,  if  the  force  were 
applied  by  increments  increasing  gradually  from  zero  to  W. 

Combining  eqs. 


and  eliminating  Z',  we  get 

,  W2L 
*  E~A> 

whence  it  is  seen  that  the  work  expended  upon  the  elongation 
of  the  bar  varies  directly  with  the  square  of  the  force  pro- 
ducing it,  with  the  length  of  the  bar,  and  inversely  with  the 
area  of  cross  section  and  coefficient  of  elasticity. 


TENSION. 


85 


Elongation  of  a  bar,  its  -weight  considered. 

161.  To  determine  the  elongation  of 
a  bar,  under  the  same  circumstances 
as  the  preceding  case,  when  its  weight 
is  taken  into  consideration. 

In  eq.  (2),  the  weight  of  the  bar 
being  very  small  compared  with  W,  it 
was  neglected. 

To  determine  the  elongation,  con- 
sidering the  weight  of  the  bar,  repre- 
sent (Fig.  13)  by  L,  W,  I,  and  A,  the 
same  quantities  as  before,  by  a?,  the 
distance  from  A  of  any  section  as  C, 
by  dx,  the  length  of  an  elementary 
portion  as  C  D,  and  by  w,  the  weight 
of  a  unit  of  volume  of  the  bar.  The 
volume  of  the  portion  B  C,  will  be  ex- 
pressed by  (L— a?)  A ;  and  its  weight 
by  (L— x)  Aw.  FIG.  13. 

The  total  force  acting  to  elongate  the  elementary  portion 
C  D,  will  be  expressed  by 

W  -f  (L  —  x)  Aw. 
Substituting  this  for  W,  and  dx  for  L  in  eq.  (2),  we  have 


elongation  of  dx  = 


—  x)  Aw 


, 
dx. 


The  total  length  of  dx  after  elongation  will,  therefore,  be 

,        W+(L  —  x)  Aw, 
EA 

Integrating  this  between  the  limits  x  =  0  and  SB  =  L,  there 
obtains, 

WL 


L  +  1  = 


.    .     .    .     (7) 


for  the  total  length  of  the  bar  after  elongation 
This  may  be  written, 


flfi  CIVIL   ENGINEERING. 

If,  in  this  expression,  we  make  W  =  0,  we  have 


In  this,  wAL  is  the  weight  of  the  bar;   representing  this 
weight  by  W  and  substituting  in  last  expressson,  we  have 


EA 

or  the  elongation  due  to  the  weight  of  the  bar,  is  one  half  of 
what  it  would  be  if  a  weight  equal  to  that  of  the  bar  were 
concentrated  at  the  lower  end. 

An  examination  of  the  expression,  W+  (L  —  x)  Aw,  shows 
that  the  strain  on  the  different  cross-sections  varies  with  x, 
decreases  as  x  increases,  and  is  greatest  for  x  =  0,  or  on  the 
section  at  the  top.  Since  the  bar  has  a  uniform  cross-section, 
the  strain  on  the  unit  of  area  is  different  in  each  section. 


BAB  OP  UNIFORM  STRENGTH  TO  RESIST  ELONGATION. 

162.  To  determine  the  form  a  vertical  bar  should  have,  in 
order  to  be  equally  strong^  throughout,  when  strained  only  ~by 
a  force  acting  in  the  direction  of  the  axis  of  the  bar,  the 
weight  of  the  bar  being  considered. 

Suppose  the  bar,  fixed  at  one  end  aiid  the  applied  force 
producing  elongation  to  be  a  weight  suspended  from  the 
other  end.  [Fig.  14] 

From  the  preceding  article,  it  is  seen  that  if  the  bar  has  a 
uniform  cross-section,  that  the  strain  on  each  section  is  dif- 
ferent. In  order  that  the  bar  should  be  equally  strong 
throughout,  the  strain  on  each  unit  of  area  of  cross-section 
must  be  the  same  throughout  the  bar.  This  can  only  be 
effected  by  making  the  area  of  the  cross-section  proportional 
to  the  stress  acting  on  it,  or  having  the  cross-sections  variable 
in  size. 

Represent  by 

A,  the  area  of  the  variable  cross-section ; 

A',  the  area  of  cross-section  at  B,  or  the  lower  one ; 

A",  the  area  of  cross-section  at  A,  or  the  top  section^; 

T,,  the  strain  allowed  on  the  unit  of  area ; 

W,  the  force  applied  to  the  bar  producing  elongation ; 

a?,  the  distance,  B  C,  estimated  upwards  from  B. 


TENSION. 


87 


The  total  force  acting  on  any 
section  as  C,  to  elongate  it,  is 


W+w 


w  being  the  weight  of  the  nnit 
of  volume  of  the  bar. 

Since  T,  is  the  strain  allowed 
on  the  unit  of  area,  T,  x  A  will 
represent  the  total  strain  on 
the  section  at  C,  and  will  be 
equal  to  the  force  acting  on  this 
section  to  elongate  it.  Hence, 
we  have 


(8) 


Differentiating,  we  have 

wAdx  =  T^A, 
which  may  be  written 
wdx_dA. 

^rr=x' 

Integrating,  we  get 

wx 

-TT  =Nap.  log  A+C. 


(9) 


Making  x  =  0,  we  have  A  =  A',  whence 


Substituting  for  C  in  eq.  (9)  its  value  obtained  from  the 
last  equation,  we  get 


=  tfap.log-^ 
and  passing  to  the  equivalent  numbers, 

W 


But 


A'= 

which  substituted  above  gives, 


33  CIVIL   ENGINEERING. 

Making  x  =  L  and  A  becomes  equal  to  A",  hence 
A"-  W  ^ 

A     —  7p-0 

•*-! 

the  value  for  the  area  of  the  section  at  the  upper  end. 

Form  of  bar  when  it  has  a  circular  cross-section. 

163.  No  particular  form  has  been  assigned  to  the  cross  sec 
tion  of  the  bar  in  this  discussion.  Let  it  be  a  circle  and  rep 
resent  the  variable  radius  by  r. 

Then  the  area  of  any  cross-section  will  be  TT/**,  which  being 
substituted  for  A  in  eq.  (8),  gives 


W  +  w  Cn^dx  =  TjTiT9. 


Differentiating,  there  obtains 

W7rr*dx  = 
hence 

dr_       w 

~  "2T, 
which  integrated  gives 

Nap.  log.  r  =  j^x  +  0,    .    .     (10) 

which  shows  the  relation  between  x  and  r. 

Eq.  (10)  is  the  equation  of  a  line,  which  line  being  con- 
structed will  represent  by  its  ordinates  the  law  of  variation  of 
the  different  cross-sections  of  the  bar.  It  also  shows  the  kind 
of  line  cut  from  the  bar  by  a  meridian  plane. 

The  most  useful  application  of  this  problem  is  to  determine 
the  dimensions  of  pump-rods,  to  be  used  in  deep  shafts,  like 
those  of  mines. 


COMPRESSION. 

164.  The  strains  caused  by  pressure  acting  in  the  direction 
of  the  axis  of  the  piece  tend  to  compress  the  fibres  and  shorten 
the  piece. 


DEPRESSION.  89 

From  the  principle  thatv  all  bodies  are  elastic,  it  follows 
that  all  building  materials  are  compressible. 

Within  the  limit  of  elasticity  it  is  assumed  that  the  resist- 
ances to  compression  are  the  same  as  tension.  They  are  not 
really  the  same ;  but  within  the  elastic  limit  the  differences 
are  so  small,  that  for  all  practical  purposes  it  is  sufficiently 
exact  to  consider  them  equal. 

The  coefficient  of  elasticity  of  the  material  is  assumed  the 
same  in  both  cases,  and  to  distinguish  it  from  the  coefficients 
of  elasticity  when  the  fibres  are  displaced  in  other  ways,  it  is 
sometimes  called  the  coefficient  of  longitudinal  elasticity, 
or  resistance  to  direct  lengthening  or  shortening. 

To  ascertain  the  force  under  which  a  given  piece  would  be 
crushed,  we  first  ascertain  the  weight  necessary  to  crush  a 
piece  of  the  same  material ;  and  since  experiment  has  shown 
that  the  resistances  of  different  pieces  of  the  same  material  to 
crushing  are  nearly  proportional  to  their  cross-sections,  the 
required  force  can  be  easily  determined. 

Assuming  that  these  resistances  are  directly  proportional 
to  the  cross-sections,  let  W  be  the  required  force,  A  the  area 
of  cross-section  of  given  piece,  and  C  the  force  necessary  to 
crush  a  piece  of  the  same  material  whose  cross-section  is 
unity. 

We  have,  W' :  C  ::  A:l,or 

W7  =  AC, (11) 

hence  JP  =  C .  (12) 

A. 

Many  experiments  have  been  made  on  different  materials 
to  find  the  value  of  C,  and  the  results  tabulated.  If  the  ex- 
periments for  finding  C  were  not  made  on  pieces  whose 
cross-sections  were  unity,  they  were  reduced  to  unity  by 
means  of  eq.  (12).  The  pieces  used  in  the  experiments 
were  short,  their  lengths  not  being  more  than  five  times  their 
diameter  or  least  thickness. 

This  value  of  C,  the  modulus  of  crushing,  is  equal 
therefore  to  the  pressure,  upon  the  unit  of  surface,  necessary 
to  crush  a  piece  whose  length  is  less  than  five  times  its  least 
thickness,  the  pressure  being  uniformly  distributed  over  the 
cross  section  and  acting  in  the  direction  of  the  length  of  the 
piece.  Experiment  shows  that  it  requires  a  much  less  press- 
ure to  crush  apiece  when  the  force  is  applied  across  the  fibres, 
than  when  it  is  applied  in  the  direction  of  their  length. 
-  165.  The  following  are  the  values  of  C  for  some  of  the  ma- 


90  CIV  ILi  ENGINEERING. 

terials  in  common  use,  and  were  obtained  by  crushing  pieces 
of  small  size,  and  as  a  rule  not  longer  than  twice  their  diame 
ter: 

Material  Crushing  Forces  per  sq.  inch,  in  Ibs. 

Ash 4,475  to  8,783 

Chestnut 5,000 

Cedar 5,970 

Hickory 5,492  "  11,213 

Oak,  white 5,800  «  10,058 

Oak,live 6,530 

Pine 5,017  «  8,947 

Fir 6,644  «  9,217 

Hemlock 6,817 

Cast  iron 56,000  «  105,000 

Wrought  iron 30,000  «  40,000 

Cast  steel 140,000  "  390,000 

Brick 3,500  "  13,000 

Granite 5,500  "  15,300 

Rankine  gives  from  550  to  800  for  common  red  brick,  and 
1,100  for  strong  red  brick. 

The  remarks  relative  to  the  specimens  of  wood  used  to 
obtain  the  values  of  T  in  the  table  on  page  83  apply  equally 
to  this  case. 


SHEARING   STRAINS. 

166.  There  are  two  kinds  of  simple  shear ;  one  in  which 
the  stress  acts  normally  to  all  the  fibres,  like  that  developed 
in  a  rivet  when  the  plates  which  it  fastens  are  strained  by 
tension  or  compression  in  the  direction  of  their  lengths  ;  and 
one  in  which  the  stress  acts  in  a  plane  parallel  to  the  fibres, 
either  in  the  direction  of,  or  across,  the  fibre.  The  former  is 
called  a  transverse  shear,  and  the  latter,  detrusion. 

The  relations  between  the  strains  and  the  stresses  devel- 
oped by  a  shearing  force  may  be  expressed  by  equations 
analogous  to  those  used  for  tension. 

In  describing  the  shearing  strain,  the  section  C  D  (Fig.  15) 
was  supposed  not  to  have  rotated  around  any  line  in  its 
plane,  but  to  have  had  a  motion  of  translation  parallel  to 
the  plane  A  B,  so  that  after  the  movement,  any  fibre,  as 
dbt  will  have  a  new  position,  as  ab'. 


SHEARING   STRAIN. 


91 


Suppose  A  B  to  remain  fixed,  and  represent  by 

L,  the  original  length  of  any  fibre  ab 
between  the  two  consecutive  planes  A  B 
and  C  D ; 

y,  the  distance  W  which  every  point 
of  the  plane  C  D  has  moved  in  the 
direction  of  C  D,  relatively  to  the 
plane  A  B,  owing  to  the  force  causing  FIG.  15. 

this  displacement ; 

5,  the  amount  of  shearing  stress  in  any  fibre ; 

a,  the  area  of  the  cross-section  of  the  fibre ; 

E',  a  constant. 

Then, 

— =  the  intensity  of  the  shearing  stress  on  a  unit  of  area, 

and  -£-=  the  measure  of  displacement  of  the  fibre  per  unit 
of  length.     Hence, 

-  =  E'-f (13) 

a          L 

from  which  we  get 


E'= 


a  value  analogous  to  that  obtained  for  E  in  equation  (1). 

This  value  of  E'  is  constant  within  the  limit  of  elasticity 
for  each  elementary  fibre.  If  the  material  is  homogeneous 
it  has  the  same  value  for  all  the  fibres,  or  is  constant  for  the 
same  material. 

Represent  by  St  the  total  stress  developed  in  the  section 
CD;  by  A,  the  area  of  the  section ;  and  let  the  piece  be  of 
homogeneous  material.  Then, 


(14) 


which  expresses  the  relation  between  the  total  stress  de- 
veloped in  the  section  and  the  shearing  strain. 

The  constant  E'  is  the  coefficient  of  elasticity  correspond- 
ing to  a  transverse  shearing  strain,  and  is  frequently  called 
the  coefficient  of  lateral  elasticity,  to  distinguish  it  from 
the  coefficient  of  longitudinal  elasticity. 


02  CIVIL    ENGINEERING. 

The  shear  is  assumed  to  be  distributed  uniformly  over  the 
cross-section  of  the  material.  Suppose  the  shear  to  be  in- 
creased until  rupture  takes  place  and  let  S  represent  the  in- 
tensity  of  the  total  shearing  stress  on  the  cross-section. 


Then, 


in  which  S  is  the  modulus  of  shearing  for  the  material 

167.  The  following  are  some  of  the  values  of  S,  obtained 
by  experiment,  for  some  of  the  building  materials  in  use,  viz.  : 


TRANSVERSE    SHEARING. 
Materials.  Value  of  S. 

Ash G,2801b8. 

Cedar -. 3,400  « 

Hickory 6,500  « 

Oak,  White 4,000  « 

Oak,  Live 8,000  « 

Pine,  Yellow. 4,500  « 

Pine,  White 2,500  « 

Cast  steel 92,400  « 

Wrought  iron 50,000  " 

Cast  iron 30,000  « 

Copper 33,000  " 

DETRUSION. 

White  pine 480  Ibs. 

Spruce ^ 470    « 

Fir 592   « 

Hemlock 540    " 

Oak 780   " 

TRANSVERSE   STRAIN. 

168.  Extraneous  forces  acting  either  perpendicularly  or 
obliquely  to  the  axis  of  a  piece  that  is  fixed,  cause  cross- 
strains  and  develop  transverse  stresses  in  the  material. 

In  describing  the  nature  of  a  cross-strain  (Art.  150),  it  is 
assumed  that  a  consecutive  section  of  the  piece,  as  C  D  (Fig. 
16),  could  not  take  a  position  as  C'  D'  unless  the  fibres  on 
one  side  of  the  axis  of  rotation  were  lengthened  and  those 
on  the  other  side  shortened.  Also,  that  the  fibres  farthest 
from  this  axis  were  elongated  or  shortened  more  than  those 


TRANSVERSE    STRAIN.  93 

nearest  to  it,  and  as  a  consequence  the  stresses  in  the  fibres 
were  variable  in  their  intensities  throughout  the  cross-sec- 
tion. 

To  determine  the  relations  between  the  strains  of  the 
fibres  caused  by  the  bending  forces  and  the  corresponding 
stresses  developed,  a  theory  must  be  adopted  relating  to  the 
strains  produced,  and  a  law  assumed  for  the  distribution  of 
the  stresses  over  the  cross-section. 

Suppose  a  piece  of  homogeneous  material,  in  form  of  a 
bar  or  beam,  to  be  placed  in  a  horizontal  position  and  fixed 
at  one  end,  and  suppose  this  piece  to  be  acted  upon  by  a  sys- 
tem of  extraneous  forces,  the  resultant,  W,  of  which  is  per- 
pendicular to  the  axis  and  intersects  it  at  the  free  end. 

The  action  of  this  system  of  extraneous  forces  is  to  bend 
the  piece,  causing  cross-strains  and  developing  both  trans- 
verse and  shearing  stresses  throughout  the  piece. 

Neglecting  the  shearing  stress  for  the  present,  let  it  be 
required  to  determine  the  relations  between  the  cross-strains 
and  the  transverse  stresses  produced  by  the  lending  force,  W. 
•  The  cross-sections  of  the  piece  are  assumed  to  be  uniform, 
or  to  vary  from  each  other  by  some  law  of  continuity  that  is 
known  ;  the  forms  of  the  cross-sections  are  similar,  and  for 
any  two  consecutive  sections  may  be  considered  to  be  equal. 

The  common  theory  for  the  strains,  deduced  from  obser- 
vation and  experiment,  is  as  follows,  viz. : 

1.  That  the  fibres  on  the  convex  side  of  the  piece  are  ex- 
tended, and  those  on  the  opposite  side  are  compressed. 

2.  That  the  strains  of  the  fibres  caused  by  the  bending 
force  are  either  compressive  or  tensile. 

3.  That  there  is  a  surface  between  the  compressed  and  ex- 
tended fibres  in  which  the  fibres  are  neither  compressed  nor 
extended. 

4.  That  the  strains  of  the  fibres  are  proportional  to  their 
distance  from  this  surface,  known  as  the  neutral  surface. 

5.  That   the   cross-sections  of  the  piece    normal  to   the 
fibres  before  bending  will  remain  normal   to   them   after 
bending. 

6.  That  rupture  will  take  place  either  by  compression,  or 
by  extension,  of  the  fibres  on  the  surface  of  the  piece  when 
the  stress  is  equal  to  the  modulus  of  rupture. 

The  intersection  of  the  neutral  surface  by  the  plane  of 
cross-section  is  called  the  neutral  axis  of  the  section. 

From  this  theory,  it  follows,  that  the  intensities  of  the 
stresses  of  tension  "and  compression  in  the  fibres^  are  also 
proportional  to  their  distances  from  the  neutral  axis  as  long 
as  the  strain  is  within  the  elastic  limit.  The  stress  devel- 


94  CIVIL  ENGINEERING. 

oped  on  a  cross-section  to  resist  the  action  of  a  bending 
force  is,  therefore,  a  uniformly  varying  one ;  being  least,  or 
zero,  at  the  neutral  axis,  and  greatest  at  the  points  farthest 
from  this  axis. 

To  find  the  stress  in  any  fibre  in  terms  of  the  strain,  let 
A  B  and  C  D  (Fig.  16)  be  the  intersections  of  two  consecutive 
cross-sections  of  the  piece  by  the  plane  of  the  axis,  E  F,  of 
the  piece  and  the  resultant,  W,  of  the  bending  forces. 


A      ( 

;  c' 

q—  b 

t 

r 

f     0 


FIG.  16. 


FIG.  17. 


Let  0  Y  and  0  Z  (Fig.  17)  be  two  rectangular  co-ordinate 
axes  to  which  all  points  of  the  cross-section  are  referred. 

Kepresent  by 

y  and  z*  the  co-ordinates  of  all  points  in  the  plane  Y  Z  ; 

a?,  the  distances  measured  on  the  line  E  F ; 

dx  =  O'O  =  the  distance  between  the  sections  A  B  and  C  D; 

dydz  =  a  =  the  cross-section  of  a  fibre ; 

A  =  be  =  the  elongation  of  any  fibre  as  abj 

p  =  0  R,  the  radius  of  curvature. 

Let  the  section  A  B  remain  fixed  and  the  section  C  D  take 
some  position  as  C'D'  under  the  action  of  the  bending  force; 
the  strain  being  within  the  elastic  limit. 

Then,  by  hypothesis,  the  fibres  above  E  F  will  be  elon- 
gated, and  the  elongation  bo  of  any  one  fibre,  as  ab,  will  be 
proportional  to  its  distance,  y,  from  the  neutral  axis. 

Irom  the  similar  triangles  bO'c  and  0  R  0'  we  have 


or, 


be  :  0  0' : :  50'  :  0  R, 

A  :  dx i : :  y  :  p, 


whence 


(15) 


an  expression  for  the  amount  of  elongation  of  a  fibre  at  the 
distance  y  from  the  neutral  axis. 

The  expression  for  the  intensity  of  the  stress  developed 


TRANSVERSE   STRAIN.  95 

in  a  bar  to  resist  an  elongation  eqnal  to  I  is  (eq.  3)  equal  to 
EA-j-.     In  this  expression  substituting  dydz  for  A,  the 

JL/ 

value  of  A  just  obtained  for  Z,  and  dx  for  L,  we  obtain    * 

E 

—  ydydz    .....     (16) 

for  the  intensity  of  the  stress  developed  in  the  fibre  db. 

Since  this  expression  is  true  for  any  fibre  that  is  elongated, 
the  total  stress  on  the  elongated  fibres  of  this  section  will  be 
expressed  by 


In  like  manner  the  total  stress  on  the  compressed  fibres  will 
be  expressed  by 


\ffydyte, 


the  negative  sign  being  used  to  denote  the  contrary  direction 
of  the  elastic  resistance  of  the  compressed  fibres. 

Since  the  strain  is  within  the  elastic  limit  the  beam  is 
strong  enough  to  resist  the  action  of  the  extraneous  forces, 
and  the  moment  of  resistance  at  the  cross-section  is  exactly 
equal  and  opposite  to  the  moment  (Wx)  of  the  bending  forces 
at  the  same  cross-  section. 

The  moment  of  resistance  to  elongation  of  a  fibre,  at  the 
distance  y  from  the  neutral  axis,  is  equal  to  the  intensity  of 
the  stress  in  the  fibre  (eq.  16)  multiplied  by  y,  and,  to  com- 
pression, the  same  expression  multiplied  by  —  y. 

The  total  moment  of  resistance  at  the  cross-section  will  be 


which  placed  equal  to  W#,  gives  an  equation  expressing  the 
relation  between  the  moments  of  the  transverse  stresses  and 
those  of  the  extraneous  forces  producing  bending  at  any 
cross-section  of  the  beam. 

Let  b  be  the  greatest  value  of  s,  and  £  d  that  of  y  (Fig. 
17)  and  integrating  expression  (17)  so  as  to  include  the  whole 
cross-section,  we  may  write  this  equation  as  follows  : 


E    S** 

PS»  =  0 


.    (18) 


96  CIVIL    ENGINEERING. 

It  will  be  seen  that  the  quantity  under  the  sign  of  inte- 
gration when  integrated  twice  will  give  the  moment  of 
inertia  of  the  cross-section  of  the  piece  with  respect  to  the 
neutral  axis.  Representing  this  by. I  and  that  of  the  extra- 
neous force  by  M,  we  may  write  (eq.  18)  as  follows: 

—  =  M.  (19.) 

P 

The  first  member  is  oftentimes  called  the  moment  of 
elasticity,  sometimes  the  moment  of  resistance,  and 
at  others  the  moment  of  flexure,  and  the  second  member 
is  called  the  bending  moment. 

169.  This  equation  may  be  verified  as  follows : 

We  know  that  if  all  the  elementary  masses  were  concen- 
trated at  the  principal  centre  of  gyration,  the  moment  of 
inertia  would  be  unaltered  ;  also,  that  the  forces  tending  to 
produce  rotation  of  the  body  might  be  concentrated  at  this 
point  without  thereby  changing  the  conditions  of  equilib- 
rium. 

Suppose  the  resistances  offered  by  the  fibres  to  rotation 
concentrated  at  the  principal  centre  of  gyration,  and  equal 
to  P'  acting  with  a  lever  arm,  L  We  have  for  equilibrium, 

Yk  =  Wx  =  M. 

From  Mechanics,  we  have 

r 
Jc  =  principal  radius  of  gyration  =A/- 

in  which  m  is  the  elementary  mass,  r  its  distance  from  the 
axis,  and  A  the  area  of  cross-section. 

Substituting  for  2  the  sign  of  integration,  and  for  m  its 
value  in  terms  of  y  and  z  (Fig.  17),  we  get, 


;&  = 


fffdydt 


A 

Squaring  and  dividing  both  members  by  £,  we  get 

fftfdydz 
~         ~ 


TRANSVERSE   STRAIN.  97 

Hence, 


and 


whence 


J  J 


J  J  y*dydz 


which  is  the  value  the  force  would  have  on  the  unit  of  area 
at  the  principal  centre  of  gyration,  or  the  distance  Jc  from  the 
neutral  axis,  under  this  hypothesis. 

It  has  been  assumed  that  the  resistances  are  directly  pro- 
portional to  the  distance  from  the  neutral  axis  ;  hence,  at  the 
unit's  distance,  the  force  on  the  unit  of  area  would  be 

E»  M 


**  "  ffy'dyfc 

and  at  the  distance,  y,  the  force  would  be 

My 


The  strain  on  the  unit  of  area  at  the  distance,  y,  from  the 

•p 

axis  is  shown  by  expression  (16),  to  be  equal  to  —  y-   Hence, 
E  My 

7?  = 

or 


which  is  the  same  result  as  that  shown  by  eq.  (18). 
7 


98  CIVIL   ENGINEERING. 


SHEARING  STRAIN    PRODUCED  BY  A  FORCE    ACTING    TO   BEND    THE 

BAR. 

170.  No  reference  was  made  in  the  preceding  article  to 
the  shearing  strain  produced  in  the  bar  by  a^  bending  force 
acting  at  one  end,  for  the  reason,  that  in  prismatic  bars  of 
this  kind  it  is  rarely  necessary  in  practice  to  consider  this 
strain. 

If  in  this  bar  (Fig.  16),  the  section  A  B  had  been  taken 
consecutive  to  the  section,  at  F,  where  the  force  was  applied, 
the  action  of  the  force  would  not  have  been  to  turn  this 
section  F  around  a  line  in  its  plane,  but  to  have  sheared  it 
off  from  its  consecutive  section.  This  action  would  have  been 
resisted  by  the  adhesion  of  the  sections  to  each  other.  The 
force  W  is  supposed  to  act  uniformly  over  the  entire  sec- 
tion F,  hence  the  resistance  to  shearing  in  the  adjacent 
section  will  be  uniformly  distributed  over  its  surface  and 
equal  to  W.  The  resistance  on  the  unit  of  surface  would 

therefore  be  -j-. 
A 

The  adhesion  of  these  two  sections  prevents  their  separa- 
tion by  this  force,  hence  the  second  section  is  drawn  down  by 
the  force  W,  which  tends  to  shear  it  from  the  third  section, 
and  so  on. 

In  this  particular  case,  the  action  of  the  force  W  to  shear 
the  sections  off,  is  transmitted  from  section  to  section  until 
the  fixed  end  is  reached,  and  the  shearing  strain  of  each  sec- 
tion is  the  same  and  equal  to  W.  And  in  general,  the  shear- 
ing stress  of  any  cross-section  of  a  bar  or  beam  placed  in 
a  horizontal*  position  is  equal  to  the  sum  of  all  the  vertical 
forces  transmitted  through  arid  acting  at  that  section. 


CHANGES   IN  FORM  OF   THE   BAR. 

171.  In  a  bar  strained  by  a  force  acting  in  the  direction 
of  its  axis,  the  lengthening  and  shortening  of  the  bar  have 
been  the  only  changes  of  form  considered.  There  is  anothei 
change  that  invariably  accompanies  them.  This  is  the  con- 
traction or  enlargement  of  the  area  of  cross-section,  when  the 
bar  is  extended  or  compressed.  When  the  elongation  or  con- 
traction is  small,  the  change  in  cross-section  is  microscopically 
small ;  but  when  these  strains  are  very  great,  this  change  is 
sensible  in  many  materials. 


TRANSVERSE   STRAIN.  99 

In  structures,  the  piecea  are  not  subjected  to  strains  of 
sufficient  magnitude  to  allow  this  change  of  cross-section  to 
be  observed,  and  hence  it  is  neglected. 

It  is  well  to  keep  this  change  in  section  in  mind,  as  by  it 
we  are  able  to  explain  certain  phenomena  that  are  met  with 
in  experiments,  when  the  strains  to  which  the  specimens  are 
submitted  pass  the  limits  of  elasticity. 


STRAIN  ON  THE  UNIT  OF  AREA  PRODUCED  BY  A  BENDING  FORCE. 

-172.  Expression  (16)  represents  the  stress  of  extension  ou 
the  fibre  whose  cross-section  is  dydz.  Dividing  this  expres- 
sion by  the  area  of  cross-section  of  the  fibre,  we  have 


in  which  P  represents  the  stress  on  the  unit  of  area  at  the 
distance  y  from  the  neutral  axis.  Dividing  through  by  y 
and  multiplying  both  members  by  I,  we  have 


p     y 

whence 


(22) 


which  formula  gives  for  a  force  of  deflection,  the  stress  on  a 
unit  of  area  at  any  point  of  the  section. 

When  the  bar  lias  a  uniform  cross-section,  I  will  be  con- 
stant, and  P  will  vary  directly  with  y  and  M,  and  by  giving 
to  y  its  greatest  value,  we  find  the  greatest  strain  in  any  as- 
sumed cross-section. 


VALUES  OF  L 


173.  In  bars  or  pieces  having  a  uniform  cross-section,  the 
moment  of  inertia  for  each  section  with  reference  to  the  neu- 
tral axis  is  the  same,  and  hence  I  is  constant  for  each  piece, 
and  is  easily  determined  when  the  section  is  a  known  geomet 
rical  figure. 


100 


JL.. 


-K 


CIVIL  ENGINEERING. 

1.  When  the  cross-section  is  a  rectangle  (Fig.  18) 
in  which  b  is  the  breadth,  and  d  the  depth,  the 
integral  taken  within  the  limits  3  =  0,  and  z  ~  &, 
y  =  4^  and  y  =  —  £d,  gives 

I  =  , 


FIG.  18. 


2.  For  a  cross-section  of  a  hollow  girder,  like  that 
of  (Fig.  19)  in  which  b  is  the  entire  breadth,  d  the  total 
depth  V  the  breadth  of  the  hollow  interior,  d'  its  depth,  the 
integral  gives 


Fie. 


the  limits 
+  ,and  — 


FIG.  20. 


The  expression  will  be  of  the  same  form  in  the 
case  of  the  cross-section  of  the  I-girder,  (Fig. 
20),  in  which  b  is  the  breadth  of  the  flanges ;  bf 
the  sum  of  breadths  of  the  two  shoulders  ;  d  the 
depth  of  the  girder,  and  d'  the  depth  between  the 
flanges. 

3.  When  the  cross-section  is  a  circle,  and  the 
axes  of  co-ordinates  are  taken  through  the  centre, 
of  s  will  be  +  r,  —  r ;  and  those  of  y  will  be 

I  =  JTT/**. 

4.  For  a  hollow  cylinder,  in  which  r  is  the 
exterior  and  r'  the  interior  radius, 


5.  When  the  cross-section  is  an  ellipse,  and 
the  neutral  axis  coincides  with  the  conjugate 
axis,  if  the  transverse  axis  be  represented  by  <#, 
and  the  conjugate  by  5,  and  the  limits  of  z  and  y 


be  taken  in  the  same  manner,  as  in  the  circle,  then, 
1  = 


6.  When  the  cross  section  is  a  rhombus  or  lozenge,  in 
which  5  is  the  horizontal  and  d  the  vertical  diagonal, 


FLEXURE. 


174.  In  the  preceding  article  on  transverse  strain,  to  sim- 
plify the  investigation,  without  affecting  the  accuracy  of  the 


FLEXURE.  101 

results,  the  bar  was  placejj  horizontally,  and  no  notice  was 
taken  of  the  change  of  position  of  the  mean  fibre  after  the 
application  of  the  bending  force. 

The  strain  was  within  the  limit  of  elasticity,  and  for  this 
force  the  body  was  regarded  as  perfectly  elastic. 

The  action  of  the  force  was  to  bend  the  bar,  and  hence  to 
bend  the  mean  fibre  without  lengthening  or  shortening  it, 
making  it  assume  a  curved  form. 

"When  the  bar  is  bent  in  this  manner,  the  curve  assumed 
by  the  mean  fibre  is  called  the  elastic  curve  or  equilibrium 
curve.  Its  equation  is  deduced  by  equating  the  moment  of 
resistance  and  the  bending  moment,  and  proceeding  through 
the  usual  steps. 

All  the  external  forces  to  the  right,  or  to  the  left,  of  any 
assumed  cross-section  are  held  in  equilibrium  by  the  elastic 
resistances  of  the  material  in  the  section. 

FT 

The  general  equation  (19),  -—  =  M,  expresses  the  condi- 
tion of  equality  between  the  moments  of  resistance  and  bend- 
ing, and  is  the  equation  from  which  that  of  the  curve  as- 
sumed by  the  mean  fibre  after  flexure  may  be  deduced. 

From  the  calculus,  we  have 


which,  substituted  in  eq.  (19),  gives 

ETv£& 

^'    M  .    (23) 


When  the  deflection  is  very  small,  -^  is  very  small  com- 

pared with  unity  and  may  be  omitted  ;  and  eq.  (23)  becomes 
for  this  supposition 


(24) 


which  is  the  general  equation  expressing  the  relation  between 
the  moment  of  flexure  and  the  bending  moment  of  the  ex- 


102 


CIVIL    ENGINEERING. 


traneous  forces  for  the  mean  fibre  of  any  prismatic  bar,  when 
the  deflection  is  small. 

175.  To  find  the  equation  of  mean  fibre  of  a  bar 
placed  horizontally,  fixed  at  one  end,  and  strained 
by  a  vertical  force  W  at  the  other  end. 

Denote  by  (Fig.  21) 
Z,  the  length  of  the  bar 
from  the  fixed  end^  to 
the  point  of  application 
of  W ,  it  will  be  equal 
to  the  length  of  the 
mean  fibre,  A  B. 

Let  AX  and  AY  be 
the  co  -  ordinate  axes 
and  Y  positive  downwards.  The  bending  moment  of  W  for 
any  point,  a?,  will  be  W  (I  —  a?),  and  substituting  this  for  M 
in  eq.  (24),  we  have 


FIG.  21. 


=  W(Z— x).     .     .     .     (25) 
-or*)  +  C.  (26) 


Integrating,  we  have 


If  x  =  0,  by  hypothesis  ~-  =  0,  and  hence  0  =  0. 
Integrating  eq.  (26)  we  have 

Ely  =  ^  (Six?  —  or*)  +  C'     .     .     (27) 
Noting  that  for  x  =  0,  y  =  0,  we  have  C'  =  0, 


hence, 


y  = 


w 


-a?)      .     .     .     (28) 


which  is  the  equation  of  the  curve  of  mean  fibre  under  these 
circumstances. 

Inspection  of  eqs.  (26  and  28)  will  show  that  the  greatest 
slope  of  the  curve  and  the  greatest  distance  between  any  point 
of  it  and  the  axis  of  X  will  be  at  B.  Eqs.  (25)  and  (28)  show 
that  the  curve  is  convex  towards  the  axis  of  X. 

Represent  by  f  the  maximum  ordinate  of  the  curve.  It8 
value  will  be  obtained  by  making  x  =  I,  hence 


(29) 


STRAINS   IN   BEAMS.  103 

If  the  bar  had  been  loaded  uniformly  instead  of  by  a 
weight  acting  at  its  extremity;  representing  by  w  the  load 
on  a  unit  of  length,  eq.  (24)  would  have  become  for  this  case, 


hence  the  equation  of  the  curve  of  its  mean  fibre, 
w 


The  value  of  the  maximum  ordinate  in  this  case  would 

wl* 


instead  of  W  concentrated  at  the  end  as  shown  by  eq. 
(28),  suppose  it  to  have  been  uniformly  distributed  over  the 

W 
bar,  then  —  would  be  the  load  on  each  unit  of  length  in  that 

L 

case,  and  substituting  this  in  eq.  (32)  for  w,  and  calling  the 
corresponding  ordinate,  f  ',  we  have, 

JVF         74 

I  WZ3 

f      ~8ET:=8EI      *    '    '     (33) 

Hence  f  \f  ;  ;  •§•  :  -J-,  from  which  we  see  that  concentrating 
the  load  at  the  end  of  the  bar  increases  the  deflection  nearly 
three  times  that  obtained  when  the  load  was  uniformly  dis- 
tributed. 


BEAMS  OF  UNIFOEM  CROSS-SECTION. 
BEAMS    RESTING  ON  TWO    OR  MORE    SUPPORTS. 

176.  The  term  bar  is  used  to  designate  a  piece  when  the 
dimensions  of  its  cross-section  are  not  only  small  compared 
with  the  length  of  the  piece,  but  are  actually  small  in  them- 
selves. The  term  beam  is  used  when  the  cross-section  is 
of  considerable  size,  consisting  of  several  square  inches. 

A  beam  resting  on  three  or  more  supports,  or  having  its 
ends  fixed  so  that  they  will  not  move  is  called  a  continuous 
beam.  If  it  rests  on  two  points  of  support  only,  and  the 
ends  are  free  to  move,  it  is  a  non-continuous  beam.  If  placed 
in  a  horizontal  position,  with  one  end  fixed  and  the  other 
free,  it  is  known  as  a  semi-girder  or  cantilever. 


104 


CIVIL   ENGINEERING. 


Beam  Resting  on  two  Points  of  Support. 

177.  Let  it  be  required  to  determine  the  bending  mo« 
ments,  shearing  stress,  and  equation  of  mean  fibre  of  a 
straight  beam  resting  in  a  horizontal  position  on  two 
points  of  support. 

There  are  two  cases :  1,  when  the  beam  is  uniformly  loaded ; 
and,  2,  when  acted  upon  by  a  single  force  between  the  two 
points  of  support. 

1st  CASE. — The  external  forces  acting  on  the  beam  are  the 
load  uniformly  distributed  over  it  and  the  vertical  reactions 
at  the  points  of  support. 


FIG.  22. 

Let  A  B  (Fig.  22)  be  the  beam,  A  and  B  the  points  of  sup« 
port,  and  A  the  origin  of  co-ordinates.  A  X  and  A  Y,  the  axes. 
Denote  by  21  the  distance  between  two  points  of  support  A  B. 

w  =  weight  on  unit  of  length. 

x  =  abscissa  of  D,  any  section  of  the  beam  A  B. 

The  total  load  on  the  beam  is  %wl  and  the  reactions  at  each 
point  of  support  are  respectively  equal  to  —  wl. 

Bending  moment. — Let  D  be  any  section  of  the  beam  made 
by  a  plane  passed  perpendicularly  to  the  axis,  through  the 
point,  whose  abscissa  is  x,  and  let  us  consider  all  the  forces  act- 
ing  on  either  side  of  D  ;  in  this  case  let  it  be  on  the  side  A  D. 

The  forces  acting  on  the  beam  from  A  to  D  are  the 
weight  on  this  portion  of  the  beam,  and  the  reaction  at  A. 
The  algebraic  sum  of  their  moments  will  be  the  bending 
moment  of  the  external  forces  acting  on  this  segment.  Let 
M  be  this  moment  and  we  have 


wx  x—  —  wl  x  x  =  — wlx     .     .     .     (34) 


STRAINS   IN   BEAMS.  105 

The  second  member  of  this  equation  is  a  function  of  a  sin- 
gle variable,  and  may  therefore  be  taken  as  the  ordinate  of  a 
line  of  which  x  is  the  abscissa.  Constructing  the  different 
values  of  the  ordinate,  the  line  may  be  traced.  This  line  is  a 
parabola,  and  shows  the  rate  of  increase  or  decrease  in  the 
bending  moments. 

The  curve  thus  constructed  may  be  called  the  curve  of  the 
bending  moments. 

Shearing  strain.  —  The  shearing  stress  in  the  beam  at  D 
is  equal  to  the  algebraic  sum  of  all  the  vertical  forces  acting 
at  this  section,  hence 

S'=  wx  —  wl  ......     (35) 

The  second  member  of  this  equation  represents  the  ordi- 
nate of  a  right  line.  Constructing  the  line,  the  ordinates  will 
show  the  rate  of  increase  or  decrease  of  the  shearing  strain 
for  the  different  sections. 

By  comparing  equations  (34)  and  (35)  it  will  be  seen  that 


which  shows  that  the  shearing  stress  at  any  section  is 
eqiial  to  the  first  differential  coefficient  of  the  bending  'moment 
of  that  section  taken  with  respect  to  x. 

For  convenience  we  used  the  segment  A  D,  but  the  results 
would  have  been  the  same  if  we  had  taken  B  D.  For,  sup- 
pose we  find  the  bending  moment  for  this  segment,  we  have 
for  the  moment  of  the  weight,  acting  to  turn  it  around  D, 


And  for  the  moment  of  reaction, 

-  wl(2l  -  x). 
The  algebraic  sum  of  these  moments  will  be 


the  same  as  (34),  as  it  should  be. 

Equation  of  mean  fibre.  —  Substituting  the  second  mem 
ber  of  eq.  (34)  for  M  in  eq.  (24),  we  have 

EI^j[  =  lswxt--wto.    .    .    (37) 
Integrating,  we  get 


106  CIVIL   ENGINEERING. 

For  £  =  £,  -^  =  0,  and  we  have  C  =  %wl\ 

dx 
Substituting  this  value  of  C,  and  integrating,  we  get 

Ely  =  —  x*—™lx*  +  ±wl3x  +  C'. 
24          6 

For  x  =  0,  y  is  equal  0,  and  hence  C'—  0,  and  we  have 


which  is  the  equation  of  the  curve  of  mean  fibre,  and  may  be 
discussed  as  any  other  algebraic  curve. 

Deflection.  —  If  we  represent  the  maximum  ordinate  of  the 
curve  by/j  we  find 


the  maximum  deflection,  which  is  at  the  middle  point  of  the 
beam. 

Equation  (38)  may  be  placed  under  the  form, 

w 

O[5Z'-(a!-Z)']     .     (39) 


For  values  of  as,  differing  but  slightly  from  Z,  the  quantity 
(x—l)*  may  be  omitted  without  materially  affecting  the  value 
of  the  second  member  for  these  values.  Omitting  this  quan- 
tity, and  eq.  (39)  reduces  to 

fo-*')  •  •  •  •  (40) 

which  is  the  equation  of  a  parabola.  Hence,  a  parabola  may 
be  constructed  passing  through  the  middle  point  of  the  curve 
of  mean  fibre  and  the  points  of  support,  which  nearly  coin- 
cides with  the  curve  of  mean  fibre  in  the  vicinity  of  its 
middle  point. 

The  parabola  whose  equation  is  eq.  (40)  differs  but  slightly 
throughout  from  the  curve  given  by  eq.  (38)  ;  for  the  greatest 

difference  between  the  ordinates  of  the  two  lines  for  the  same 

I  __ 

value  of  «,  will  be  when  x  =     (2  ±  V  2),  which  gives 


/,  representing  the  ordinate  of  the  curve  for  this  value  of  a?, 
and  y",  the  ordinate  of  the  parabola  for  the  same  value  of  » 


STRATA'S    IN    BEAMS. 


107 


"Whence,  we  get 

178.  2o  CASE. — The  external  forces  acting  oii  the  beam  are 
the  applied  force,  whatever  it  may  be,  and  the  vertical  re- 
actions at  the  points  of  support. 

Let  A  B  (Fig.  23)  represent  the  beam  resting  on  the  supports, 
A  and  B,  sustaining  a  weight,  2W,  at  any  point,  as  P,  between 
the  points  of  support.  JDenote  the  reactions  at  A  and  B  by 
R,  and  Ra,  A  B  by  2Z,  A  P  by  I'. 


2YV 


FIG.  23. 

The  reactions  R,  and  R,  will  be  proportional  to  the  segments 
in  which  the  beam  is  divided,  and  this  sum,  disregarding  the 
weight  of  the  beam,  is  equal  to  2W.  Hence, 

R, :  R, :  2W  : :  PB  :  AP  :  AB, 

from  which  proportion  we,  knowing  2W  and  £',  can  determine 
the  values  of  R,  and  R,.  Knowing  these,  we  can  obtain  the 
bending  moment  and  shearing  strain  of  any  section,  and  the 
deflection  of  the  beam  due  to  the  force  2W. 

179.  The  most  important  case  of  the  single  load  is  that  in 
which  the  load  is  placed  at  the  centre.  Suppose  2W  to  act  at 
the  centre,  then  R1=R2=  — "W.  Assume  the  origin  of  co-ordin- 
ates and  the  axis  of  X  and  Y  to  be  the  same  as  in  the  first  case. 

Bending  moment. — For  any  section  between  A  and  C  the 
bending  moment  will  be  M  =  —  Wx. 

Shearing  strain. — The  shearing  stress  on  any  section  will  be 
S'  =  ±  W. 

Equation  of  mean  fibre, — Substituting  in  second  mem- 
ber of  eq.  (24)  the  above  value  of  M,  we  have 


EI      =  - 


(41) 


Integrating,  and  substituting  for  C,  its  \  ;ilue,  ire  get 
J*9     W  , 


t08  CIVIL   ENGINEERING. 

Integrating  again  and  substituting  for  C,  its  value,  we  get 
•y  =  —^  (3P%  —  a?3),  .     .     •         •  (43) 

which  is  the  equation  of  so  much  of  the  mean  fibre  as  lies  be- 
tween the  origin,  A,  and  the  middle  point,  C. 

The  right  half  of  the  mean  fibre  is  a  curve  exactly  similar 
in  form.  Assuming  B  as  the  origin  and  the  abscissas  as  posi- 
tive from  B  towards  C,  eq.  (43)  is  also  the  equation  of  the 
right  half  of  the  curve. 

Deflection. — The  maximum  deflection  is  at  the  centre,  and  is 


- 

~  '     El 

Comparing  this  with  the  deflection  at  the  centre  in  the 
previous  case,  it  is  seen  that  the  deflection  produced  l>y  a  load 
uniformly  distributed  over  the  beam  is  Jive-eighths  of  that 
produced  by  the  same  load  concentrated  and  placed  at  the 
middle  point. 

180.  Comparison  of  strains  produced.  —  The  bending 
moment  for  any  section,  when  the  beam  is  uniformly  loaded, 
is,  eq.  (34), 

nr      war          . 
M.  =  —  —  --  wlx, 

and  when  the  beam  is  acted  upon  by  a  load  at  the  middle 
point,  is,  eq.  (41), 

M  =  —  Wx, 

Both  will  have  their  maximum  values  for  x  =  I. 
Equating  these  values,  we  have 


whence  "W"  =  —  , 

2i 

which  shows  that  the  greatest  strain  on  the  unit  of  area  of 
the  fibres,  when  the  load  is  uniformly  distributed,  is  the  same 
as  that  which  would  be  caused  by  half  the  load  concentrated 
and  placed  at  the  middle  point  of  the  beam. 


Beam  strained  by  a  uniform  load  over  its  entire 
length  and  a  load  resting  midway  between  the  two 
points  of  support. 


181.  If  a  beam  be  uniformly  loaded,  and  support  also 
load  midway  between  the  points'of  support,  the  correspondii 


a 


STRAINS  IN  TraAMR.  109 

values  for  the  strains  can  be  obtained  by  adding  algebraically 
the  results  determined  for  each  case  taken  separately. 

If  the  beam  had  other  loads  besides  the  one  at  C,  we  could 
in  the  same  manner  find  the  bending  moments,  shearing 
strains,  and  deflections  due  to  their  action.  The  algebraic 
sum  of  the  moments,  ordinates  of  deflection,  etc.,  would  give 
the  results  obtained  by  their  simultaneous  action. 


Beam  having  its  ends  firmly  held  down  on  its  sv/p- 

ports. 

182.  In  the  preceding  cases  the  beams  are  supposed  to  be 
resting  on  supports,  and  not  in  any  way  fastened  to  them. 
If  the  ends  of  the  beams  had  been  fastened  firmly  so  that 
they  could  not  move — as,  for  example,  a  beam  having  its  ends 
firmly  imbedded  in  any  manner  in  two  parallel  walls — the 
results  already  deduced  would  have  been  materially  modified. 

Let  it  be  required  to  determine  the  strains  and  equation  of 
curve  of  mean  fibre  in  the  case  where  the  beam  has  its  ex- 
tremities horizontal,  and  firmly  embedded  so  that  they  shaft 
not  move,  the  beam  being  uniformly  loaded. 

If  we  suppose  a  bar  fitted  into  a  socket  (Fig.  24)  and  acted 
upon  by  a  force  to  bend  it,  it  is  evident,  calling  Q!  the  force 
of  the  couple  developed  at  the  points  B  and  H,  that  the  mo- 
ment of  the  force  "W",  whose  lever  arm  is  I,  is  opposed  by  the 
moment  of  resistance  of  the  couple,  B  Qt  and  H  Qt  acting 
through  the  points  H  and  B. 


FIG.  24. 

Hence,  we  have 

Q/  =  AV, 

f  being  the  lever  arm  of  the  couple. 


110 


CIVIL   ENGINEERING. 


We  see  that  Q,  increases  proportionally  to  any  decrease  in 
I',  and  that  these  quantities  themselves  are  unknown,  although 
their  product  must  be  constant  and  equal  to  the  bending  mo- 
ment of  the  beam  at  B. 

To  determine  the  bending  moment  at  any  section  or  a  beam 
having  its  ends  firmly  held  down ;  let  A  B  (Fig.  25)  be  the 
beam  before  being  loaded,  and  denote  by 

21  =  A  B  =  the  length ; 

w  =  the  weight  on  unit  of  length ; 

x  —  the  abscissa  at  any  point,  the  origin  of  co-ordinates 
being  at  A,  and  A  B  coinciding  with  axis  of  X,  as  in  preced- 
ing cases. 


A         S      ,D 


C' 


Y  FIG.  25. 

The  total  load  on  the  beam  will  be  2wZ,  and  the  reactions 
at  the  points  of  support  are  each  equal  to  —  wl. 

The  bending  moment  of  any  section  D,  is  equal  to  the 
algebraic  sum  of  the  moments  of  vertical  reaction  at  A,  of 
the  weight  on  A  D,  and  of  the  unknown  couple  acting  on  the 
left  of  A. 

Calling  jjb  the  moment  of  the  unknown  couple  and  substi- 
tuting this  algebraic  sum  in  eq.  (24),  we  have 


Integrating  and  noting  that  for  x= 0,-r-= 0,  we  have  0=0, 

and 

dy         wl  ,     w 

Ln  this  equation  make  x  —  2Z,  for  which-y-=0,  and  we  find 


STRAINS   IN   BEAMS.  Ill 

which  is  the  value  of  the  moment  of  the  unknown  couple 
acting  at  the  left  point  of  support.  It  is  also  the  value  of 
the  one  at  the  right  point  of  support,  B. 

Writing  this  value  for  /z-  in  equations  (44)  and  (45),  we  have 

HJQ 

+          ...      (46) 


and  then  by  integration, 

wl         w 


We  find  C'=0,  and  substituting,  etc.,  we  get 


which  is  the  equation  of  the  curve  of  mean  fibre. 

Deflection.  —  Denoting  by  f,  the  maximum  value  for  y,  and 
we  have 


The  corresponding  value  obtained,  from  eq.  (38),  is 

.      /-&• 

A  comparison  of  these  values  of  f  shows  that  by  firmly 
fastening  the  ends  of  the  beam  to  the  points  of  support  in  a 
horizontal  position,  the  deflection  at  the  centre  is  one-fifth  of 
what  it  was  when  they  merely  rested  on  the  supports. 

Bending  moments.  —  The  curve  of  the  bending  moments  is 
given  by  the  equation. 

w  w 


which  is  that  of  a  parabola. 

The  bending  moments  for  x  =  0,  and  2Z,  are  both  equal  to 

-5-  Z2,  and  for  x  =  Z,  —  -77-  .      The  bending  moment  of  the 

section  at  the  middle  point  is  therefore  half  that  of  the  section 

w 
at  A  or  B.     Assuming  a  scale,  lay  off  -g-Z2,  below  the  line  A  3, 

on  perpendiculars  passing  through  A  and  B.     Lay  off  half  this 
value  on  the  opposite  side  of  the  line  A  B  on  a  perpendicular 


112  CIVIL   ENGINEERING. 

through  the  middle  point.  This  gives  us  three  points  of  the 
curve  of  which  one  is  the  vertex.  The  perpendicular  through 
the  middle  point  is  the  axis  of  the  parabola,  and  with  thr 
three  points  already  found  the  curve  may  be  constructed. 

This  curve  of  bending  moments  cuts  the  axis  of  X  in  two 
points,  the  abscissas  of  which  are  I  (1  ±  >/J),  and  at  the 
sections  corresponding  to  them  the  bending  moments  will  be 

equal  to  0. 

d?ii 
These  values    substituted   in  eq.  (46)  for  a?,  reduces-^ 

to  zero,  and  an  examination  of  this    equation    shows  that 

fT&i] 

there  is  a  change  of  sign  in  -r4  at  these  points.     It  therefore 

follows  that  the  curve  of  mean  fibre  has  a  point  of  inflex- 
ion for  each  of  these  values  of  a?,  that  is,  the  curve  changes 
at  these  points  from  being  concave  to  convex,  or  the  reverse, 
towards  the  axis  of  X. 

The  greatest  strains  on  the  unit  of  area  produced  by  the 
deflecting  force,  will  be  in  the  cross-sections  at  the  ends  and 
middle  ;  the  lower  half  of  the  cross-section  at  the  middle 
being  extended,  and  the  lower  halves  of  these  at  the  points  of 
the  support  being  compressed. 

Shearing  strain.  —  The  expression  for  the  shearing  force  is 

S'=  —j  —  =  wx  —  wL 
dx 

which  is  the  same  as  eq.  (35),  and  its  values  may  be  repre- 
Bented  by  the  ordinates  of  a  right  line  which  passes  through 
the  middle  point. 

The  uniform  load  concentrated  and  placed  at  the  middle. 

183.  If  instead  of  being  uniformly  loaded,  the  beam  was 
only  strained  by  a  single  load,  2W,  at  the  middle  point,  the 
bending  moment,  disregarding  the  weight  of  the  beam,  would 
be  for  values  of  x  <  I. 

M=  —  Wo?  +  IJL 
and  by  a  process  similar  to  that  just  followed,  we  would  find 


to  be  the  equation  of  the  mean  fibre  from  A  to  C. 
The  maximum  deflection  will  be 


STRAINS   IN    BEAMS. 


113 


which  is  equal  to  one-fourth  of  that  obtained,  with  a  load  at 
the  centre,  when  the  ends  of  the  beam  are  free.  It  is  also 
seen  that  the  deflection  caused  by  a  concentrated  load  placed 
at  the  middle  of  the  beam,  is  the  same  as  that  caused  by 
double  the  load  uniformly  distributed  over  the  whole  length. 
If  the  beam  was  loaded  both  uniformly  and  with  a  weight, 
2W,  the  results  would  be  a  combination  of  these  two  cases. 


Seam  loaded  uniformly,  fixed  at  one  end,  and  resting  on  a 
support  at  the  other. 

184.  Let  A  B  (Fig.  26)  represent  the  beam  in  a  horizontal 
position,  fixed  at  the  end,  A,  and  resting  on  a  support  at  the 
end  B. 


FIG.  26. 

Adopting  the  notation  used  in  previous  case,  we  have 
for  the  total  load  on  the  beam. 

The  reactions  at  A  and  B  are  unequal.  Represent  by  ^ 
the  reaction  at  A,  and  by  p  the  moment  of  the  unknown 
couple  at  A.  We  have 

I      I          .          Elg=-B^+r£+/.   .    .    (49) 
Hence  by  integration, 

a't  +  /«',0=0   (50) 


Ely  =  -  *RX+  j^tf+  /*  ~,  C'=  0    (51) 
The  bending  moment  at  B  is  equal  to  zero,  hence  for  x  =  21, 

—..  will  be  0  and  eqs.  (49)  and  (51)  reduce  for  this  value  of  x  to 
dor 

0  =  -  R$l  +  ^(llf  +  /*    .    .    .    (52) 


0=- 


f   .    (53) 


114  CIVIL   ENGINEERING. 

Combinin    these  we  find 


wl* 


Hence  the  reaction  at  B  is  %w  (2Z). 

Substituting  these  values  for  R,  and  p  in  eq.  (49)  the  bend- 
ing moment  at  any  point,  shearing  strain,  and  curve  of  mean 
fibre  can  be  fully  determined.  Placing  the  second  member 
of  eq.  (49)  equal  to  zero,  and  deducing  the  values  of  #,  these 
will  be  the  abscissas  of  the  points  of  inflexion,  and  by  placing 
the  second  member  of  eq.  (50)  equal  to  0,  the  abscissa  cor- 
responding to  the  maximum  ordinate  of  deflection  may  be 
obtained.  The  curve  of  bending  moments,  etc.,  may  be  de- 
termined as  before. 


Beam  resting  on  three  points  of  support  in  the  same  hori- 
zontal straight  line. 

185.  Let  it  be  required  to  determine  the  bending  moments, 
shearing  strain,  and  equation  of  mean  fibre  of  a  single, 
beam  resting  in  a  horizontal  position  on  three  points  of  sup- 
port, each  segment  being  uniformly  loaded. 

Let  ABC  (Fig.  27)  be  the  beam  resting  on  the  three  points, 
A,  B,  and  C. 


Fig.  27. 

Let  us  consider  the  general  case  in  which  the  segments  are 
unequal  in  length  and  the  load  on  the  unit  of  length  dif- 
ferent for  them. 

Let  I  =  A  B,  and  w,  the  weight  on  each  unit  of  its  length, 
lf=  BC,  and  w'  the  weight  on  each  unit  of  its  length 

II, ,  R2,  R3,  the  forces  of  reaction  at  the  points  of  support, 
A,  B,  and  C,  respectively. 

^Take  A  B  C  as  the  axis  of  X  and  A  the  origin  of  coordinates 
with  y  positive  downwards  as  in  the  other  cases. 

First,  consider  the  segment  A  B,  and  let  D  be  any  section 
whose  abscissa  is  x. 

Since  the  reactions  at  the  points  of  support  are  unknown, 
they  must  be  determined. 


STRAINS   IN    BEAMS.  115 

We  have 


Integrating,  we  get 

Mj=-*B^+        +  a    .    .    (55) 

Let  a  represent  the  angle  made  by  the  curve  of  mean  fibre 

with  the  axis  of  X  at  B,  then  for  x  =  I  we  havef^A    =  tan  o>, 

,  VW—  i, 

whence 

EHan«=—  iiy»  +  £i0p+0.     .    .    (56) 


Subtracting  from  preceding  equation,  member  by  member, 
we  have 


-l^.  (57) 

Integrating  eq.  (57)  we  get 
El  (y-x  tan  «)=  -  -J-  I^a*  +  ^^+  i^A  -  1  «*Zte.  (58) 

the  constant  of  integration  in  this  case  being  equal  to  0. 

If  in  eq.  (54)  we  make  x  =  I,  and  denote  the  bending  mo- 
ment of  the  section  at  B  by  /*,  we  have 

^-iy+2*  ....  (59) 

In  eq.  (58)  make  x  =  Z,  hence  y  =  0,  and  we  have 
El  tanw-|K1Z2  +  ^^  +  1^-1^=0   .   (60) 


by  omitting  common  factor  L     Combining  this  equation  with 
the  preceding  one  and  eliminating  R!  and  reducing,  we  get 

El  tan  w  =  -J  lp  —  -fowl?    .    .    (61) 

which  expresses  the  relation  between  the  tan  «  and  p. 

Going  to  the  other  segment,  taking  C  as  the  origin  of  co- 
ordinates and  calling  x  positive  towards  B,  we  may  deduce 


116  CIVIL   ENGINEERING. 

similar  relations  between  the  bending  moment  at  B  and  the 
tangent  of  the  angle  made  by  the  mean  fibre  at  B  with  the 
axis  of  X.  Since  the  beam  is  continuous,  these  curves  are 
tangent  to  each  other  at  the  point  B,  and  the  angles  made  by 
both  of  them  with  the  axis  of  X  at  that  point  are  measured  by 
a  common  tangent  line  through  B.  Therefore,  the  angles  are 
supplements  01  each  other  and  we  may  at  once  write  the  cor- 
responding relation  as  follows, 


....  (62) 

Since,  for  equilibrium,  the  algebraic  sum  of  the  extraneous 
forces  must  be  equal  to  zero,  we  have 

wl+wT— Bi— BS— B3=0      .     .    .    (63) 

and  since  the  algebraic  sum  of  their  moments  with  respect  to 
any  assumed  section  must  be  equal  to  zero,  we  have  for  the 
moments  taken  with  respect  to  the  section  at  B, 

O  O  \        / 

These  last  four  equations  contain  four  unknown  quantities, 
B!,  B-j,  BS,  and  tan  co. 

By  combining  and  eliminating,  their  values  may  be  found. 
Combining  equations  (61)  and  (62),  and  eliminating  tan  co,  we 
have 


+  w'l* 


i/      i      i/ 

The  bending  moment  of  any  section,  as  D,  is  from  equa- 
tion (54) 


hence  for  x  —  I,  we  have  M  equal  to  the  bending  moment  at 
B,  which  has  been  represented  by  /*,  or  eq.  (59) 


from  which  we  get 


-p  __  wl       n       wl 

•"     ~-  :" 


In  a  similar  way,  the-  value  of  BS  may  be  found.  These 
values  of  B!  and  K-J  substituted  in  eq.  (63),  will  give  the  value 
of  Bo. 


STRAINS   IN   BEAMS.  117 

The  external  forces,  all  being  known,  the  bending  moments, 
shearing  strain,  and  equation  of  mean  fibre  may  be  deter- 
mined as  in  previous  examples. 

186.  Example. 

The  most  common  case  of  a  beam  resting  on  three  points 
of  support,  is  the  one  in  which  the  beam  is  uniformly 
loaded  throughout  and  the  intermediate  support  is  placed  at 
the  middle  point. 

In  this  case,  I  =  I'  and  w  =  ID'.  Substituting  these  values, 
in  the  expressions  for  p  and  Rj,  we  have 


and  R!  =  £  wZ. 
The  reaction  at  the  middle  point  will  therefore  be 

or 


Substituting  the  value  of  E!  in  eq.  (54)  we  obtain  the  bend- 
ing moment  for  any  section. 

In  the  case  of  a  beam  resting  on  two  supports,  Fig.  (22),  and 
having  a  weight  uniformly  distributed  along  its  length,  it  has 
been  shown  that  each  support  bears  one  half  of  the  distributed 
load  ;  and  that  the  deflection  of  the  mean  fibre  at  the  middle 
point,  represented  by^J  is  the  same  as  the  beam  would  take 
were  fths  of  the  load  acting  alone  at  the  middle  point.  In 
the  latter  case  the  pressure  upon  a  support,  just  in  contact 
with  the  beam  at  its  middle  point,  would  be  zero  ;  and  if  the 
support  were  to  be  raised  so  as  to  bring  the  middle  of  the 
beam  into  the  same  right  line  with  the  extreme  supports, 
tho.  intermediate  support  would  evidently  sustain  the  total 
pressure  at  C  to  which  the  deflection  was  due,  and  which  was 
f  ths  of  the  entire  load  ;  hence  the  reaction  of  the  middle  sup- 
port will  be  equal  to  fths.  This  conclusion  agrees  with  the 
result  determined  by  the  previous  analysis. 

Each  segment  of  the  beam  in  this  case  might  have  been 
regarded  as  a  beam  having  one  end  fixed  and  the  other  rest- 
ing on  a  support;  a  case  which  has  already  been  consid- 
ered. 


Theorem  of  Three  Moments. 

187.  From  the  preceding,  it  is  seen,  that  the  reactions  at 
the  points  of  support  can  be  determined  whenever  we  know 
the  bending  moments  at  these  points.  These  moments  are 
readily  found  by  the  "  theorem  of  three  moments." 

This  theorem  has  for  its  object  to  deduce  a  formula  express- 


118  CIVIL   ENGINEERING. 

ing  the  relation  between  the  bending  moments  of  a  beam 
at  any  three  consecutire  points  of  support,  by  means  of  which 
the  bending  moments  at  these  points  may  be  obtained,  with- 
out going  through  the  tedious  operations  of  combination  arid 
elimination  practised  in  the  last  example. 

Take  any  three  consecutive  points  of  support,  as  A,  B,  and 


FIG.  28. 


C,  Fig.  (28),  of  a  beam  resting  on  n  supports.  Denote  by  I 
and  I',  the  lengths  of  the  segments,  A  B  and  B  C,  w  and  wf, 
the  weights  on  each  unit  of  length  in  each  segment  and 
ML  M2  M3,  the  bending  moments  at  these  points,  A,  B,  C. 

The  formula  expressing  the  relation  between  these  bending 
moments  is 


V)  4-  M8Z'  =  JwZ3  +  %w'l'\    (67) 

In  every  continuous  beam,  whose  ends  are  not  fixed,  the 
bending  moments  at  the  end  supports  are  each  equal  to  zero. 
Hence,  by  the  application  of  this  formula,  in  any  given  case, 
as  many  independent  equations  can  be  formed  as  there  are 
unknown  moments,  and  from  these  equations  the  moments 
can  be  determined. 

188.  The  demonstration  of  this  theorem  depends  upon  the 
principle,  that  the  bending  moment  at  any  point  of  support 
whatever,  and  the  tangent  of  the  angle  made  by  the  neutral 
fibre  with  the  horizontal  at  that  point,  may  be  expressed  in 
functions  of  the  first  degree  of  the  bending  moment  at  the 
preceding  point  of  support,  and  the  tangent  of  the  angle 
made  by  the  neutral  fibre  with  the  horizontal  at  that  point. 

Let  A  B  (Fig.  29)  be  any  segment  of  a  beam  resting  on  n 
supports,  A  the  origin,  A  X  and  A  Y  the  axes  of  co-ordinates, 
and  Mj  and  M2  the  bending  moments  at  A  and  B. 


FIG.  29. 

The  applied  forces  acting  on  the  beam  and  the  reactions 
are  taken  vertical  and  in  the  plane  of  the  mean  fibre. 


STRAINS   IN   BEAMS.  119 

The  external  forces  which  act  on  the  beam  to  the  left  of 
the  support,  A,  may  be  considered  as  replaced  by  a  resultant 
moment  and  a  resultant  shearing  force,  without  disturbing 
the  equilibrium.  This  resultant  moment,  represented  by  Mt, 
is  equal  and  opposite  to  the  moment  of  the  internal  forces 
at  the  section  through  the  support  A  ;  the  vertical  force, 
which  we  represent  by  Si,  is  equal  and  opposed  to  the  shear- 
in<r  force  at  this  section. 

Represent  by  fi  the  algebraic  sum  of  the  moments  of  the 
external  forces  acting  on  the  beam  between  A  and  any  section 
as  D,  whose  abscissa  is  x. 

Then  from  eq.  (24)  we  have 

El  ^  =  Mi  +  /i  +  S^   .     .     .     (68) 

Denoting  by  <j>  the  angle  which  the  neutral  fibre  after  de- 
flection makes  with  the  axis  of  X,  at  A,  and  integrating,  we 
have 


El  l^L  -  tan  6\  =  M^  +    Aafej  +  iS^.  (69) 
\ax  1  JQ 

\ 

rx 

Representing  the  quantity   I  vdx  by  M'  and  integrating, 

•'A 


we  have 

El  (y  -  x  tan  <£)  =  JM^  +   fWdx+^S^.  (70) 


0 

In  these  three  equations,  make  x  =  I  and  denote  by  N",  Q, 

a? 

and  K  what  /*,  M',  and  /  Wdx  become  for  this  value  of  a?, 
•JO 

and  by  to  the  angle  made  by  the  curve  of  mean  fibre  with 
the  axis  of  X  at  B ;  noting  that  for  x  =  I,  El  ^  =  M2,  we 

Inure 

M;  =  M!  +  N  +  SA  ] 

El  (tan  «  -  tan  ^)  =  M^  +  Q  +  iS^,  J.  (71) 
—  EB  tan  </>  =  JM/  +  K  4-  -JS/.  j 


120  CIVIL  ENGINEERING. 

Combining  the  first  and  third,  and  then  the  second  and  third 
of  these  equations  and  eliminating  S1?  we  have 


+  EK  tan  <f>  =  -  JM^  -f  %~NP  -  K, 
JEKtanw  +  fEB  tan  0  =  -  -JM^  +  £QZ  -  K         ' 


In  these  equations,  N",  Q,  and  K  depend  directly  upou  the 
applied  forces,  and  are  known  when  the  latter  are  given. 
But  Mi,  M2,  tan  </>  and  tan  o>  are  unknown. 

An  examination  of  equations  (72)  shows  that  Mg  and  tan  « 
are  functions  of  the  first  degree  of  Mj  and  tan  <£,  whatever 
be  the  manner  in  which  the  external  forces  are  applied. 

Let  us  impose  the  condition  that  the  system  of  forces  acting 
on  the  beam  shall  be  a  load  uniformly  distributed  over  each 
segment,  and  denote  by  w  the  load  on  a  unit  of  length  of  the 
segment  A  B. 

For  this  case  we  have 


J  M  dx  = 


0 
and  in  these,  by  making  x  =  Z,  we  have 

Q  = 


Substituting  in  equations  (72)  these  values  for  N,  Q,  and 
we  have 


M2  =  -  2Mi -  tan 


\ 

1(73) 


^  wP 

which  agree  with  the  principle  already  enunciated. 

189.  To  deduce  formula  (67),  let  A,  B,  C  (Fig.  28)  be  any 
three  consecutive  points  of  support  of  a  beam  resting  on  n 
supports. 


STRAINS   IN  BEAMS.  121 

From  the  first  of  equations  (73)  we  may  at  once  write 


M8  =  -  2M2  -  —  tan  f  +  W\ 

and  by  considering  x  positive  from  B  to  A,  and  giving  the 
proper  sign  to  tan  <f>  ,  we  write 

6EI 
M!  =  —  2M3  +  -y-  tan  <j>'  +  fyoP. 

Multiplying  these  respectively  by  I'  and  by  I,  and  adding 
them  together,  we  have 

M^  +  2M2  (I  +  Z')  +  M/  =  %wP+  Jw'J* 

which  expresses  the  relation  between  the  bending  momenta 
for  any  three  consecutive  points  of  support,  and  is  the  same 
as  formula  (67). 

By  a  similar  process  we  can  find  an  equation  expressing 
the  relation  between  the  tangents  of  the  angles  taken  at  the 
three  points  of  support. 

Applications  of  Formula  (67). 

190.  IST  CASE.  —  Seam  in  a  horizontal  position,  loaded 
uniformly,  resting  on  three  points  of  support,  the  segments 
being  of  equal  length. 

In  this  case,  we  have  I'  =  I,  w'  =  w,  and  Mx  and  M8  each 
equal  to  zero.  Substituting  these  values  in  eq.  (67),  we  get 


whence 

M2  = 

The  bending  moment  of  the  section  at  B  is,  eq. 


whence  we  get  for  the  reaction  at  A, 

B,  =  |*rf, 

*hich  is  the  same  value  before  found.     The  reaction  at  C  ia 


122  CIVIL   ENGINEERING. 

the  same,  and  that  at  B  can  now  be  easily  determined,  from 
the  equation, 


Knowing  all  the  external  forces  acting  on  the  beam,  the 
bending  moment  at  any  section,  the  shearing  strain,  etc.,  can 
be  determined. 

191.  2D  CASE.  —  Beam  in  a  horizontal  position  resting  on 
four  points  of  support. 

Ordinarily  a  beam  resting  on  four  supports  is  divided 
into  three  unequal  segments,  the  extreme  or  outside  ones 
being  equal  to  each  other  in  length,  and  the  middle  one 
unequal  to  either. 

If  we  suppose  this  to  be  the  case,  represent  by  A,  B,  C,  and 
D  the  points  of  support  in  the  order  given.  The  bending 
moments  at  A  and  D  are  each  equal  to  zero.  To  find  those 
at  B  and  C,  take  the  general  formula  (67)  and  apply  it  first 
to  the  pair  B  C  and  B  A,  and  then  to  the  pair  C  B  and  C  D,  and 
determine  the  bending  moments  from  the  resulting  equa- 
tions. Having  found  them,  the  reactions  are  easily  found  ; 
and  knowing  all  the  forces  acting  on  the  beam,  the  bending 
moments,  shearing  strains,  and  curve  of  mean  fibre  may  be 
obtained. 

192.  SD  CASE.  —  Beam  in  a  horizontal  position  resting  on 
five  points  of  support,  the  segments  being  equal  in  length. 

When  the  number  of  supports  is  odd,  the  segments  are 
generally  equal  in  length,  or  if  unequal,  they  are  symmetri- 
cally disposed  with  respect  to  the  middle  point. 

If  the  beam  be  uniformly  loaded,  it  will  only  be  necessary 
to  find  the  bending  moments  at  the  points  of  support  of  either 
half  of  the  beam,  as  those  for  corresponding  points  in  the 
other  half  will  be  equal  to  them. 

Suppose  the  case  of  five  points  of  support. 

Let  A,  B,  C,  D,  and  E  be  the  points  of  support,  C  being  the 
centre  one.  Eepresent  by  I  the  length  of  a  segment,  w  the 
weight  on  a  unit  of  length,  M2,  M8,  M4,  the  bending  moments 
at  B,  C,  and  D,  and  the  forces  of  reaction  at  A,  B,  and  C,  by 
RU  -R*},  Eg  respectively.  From  the  conditions  of  the  problem, 
M2  is  equal  to  M^  and  .the  reactions  at  A  and  B  are  equal  to 
the  reactions  respectively  at  E  and  D. 


STRAINS   IN    BEAMS.  128 

Applying  formula  (67)  to  the  first  pair  of  segments,  we  have 


and  applying  it  to  the  second  pair,  BC  and  CD,  we  get 


In  these  equations,  making  M^  equal  to  Ma  and  combining 
the  equations,  we  find 

M2  =  -fewfi,  and  M3  = 


The  external  forces  acting  on  the  first  segment,  AB,  to  turn 
it  around  the  section  at  B,  are  — K!  and  wl.    Hence  we  have 


whence 


The  external  forces  acting  to  turn  the  segment  A  C  or  half 
the  beam  around  C  are  the  reactions  at  A  and  B  and  the  loads 
on  the  two  segments  A  B  and  B  C. 

The  algebraic  sum  of  the  moments  for  the  section  at  C  is, 


Substituting  in  this  the  value  just  found  for  R!  and  solving 
with  respect  to  B^  we  get 


The  sum  of  the  reactions  is  equal  to  the  algebraic  sum  of 
the  applied  forces,  hence, 


R!  +  R.J  +  ES  +  K4  +  Kg  =  2Ri  +  2R2  +  ES  = 
in  which  substituting  for  R!  and  E.J,  their  values,  we  find 


The  external  forces  acting  on  the  beam  are  now  all  known, 
and  hence  the  bending  moments,  shearing  strain,  etc.,  may  be 
determined. 

193.  4:TH  CASE.  —  Seam  in  a  horizontal  position,  resting  on 
R  points  of  support  ,  the  segments  being  equal  in  length. 

If  the  beam  be  uniformly  loaded,  it  will,  as  in  the  last  case, 
only  be  necessary  to  find  the  bending  moments  at  the  points 
of  support  of  either  half  of  the  beam. 


124  CIVIL  ENGINEERING. 

If  n  be  even,  the  reaction  of  the  %nth  and  (Jfi  +  l)01  support 
will  be  equal;  if  n  be  odd,  the  i(rc+l)  will  be  the  middle 
support,  and  the  reactions  of  the  supports  equidistant  from  the 
middle  point  will  be  equal. 

The  formula  for  the  segments  would  become,  n  being  even, 

-M8  = 


##**## 
Mift  +  4Min+  !+  M^  +  2  — 

In  the  last  equation,  Min  +  1  and  MJn  +  2  would  be  equal 
espectively  to  Min  and  Min_!. 
From  these  equations,  K^  Eg,  Eg,  .  .  .  Rn  could  be  obtained. 

General  Exam/pie. 

194.  STH  CASE.  —  Beam  in  a  horizontal  position  resting  on 
n  +  ~L  points  of  support,  segments  unequal  in  length,  and 
uniform  load  on  unit  of  length  being  different  for  each  seg- 
ment. 

Kepresent  the  points  of  support  by  Ax  A9  A,  .  .  .  A,,  An  +  19 
and  the  respective  bending  moments  at  these  points  of 
support  by  M1?  M2,  M3,  .  .  .  .  Mn,  M«  +  i.  Kepresent  the 
length  of  the  segments  by  ^,  £,,  Z8,  .  .  .  .  ln  and  the  respective 
units  of  weight  on  the  segments  by  w^  w^  w^  .  .  .  .  wn. 

The  bending  moments  M1?  1^  +  ±  being  those  at  the  ex- 
tremities, are  each  equal  to  zero,  and  therefore  there  are  only 
Ti—1  unknown  moments  to  determine.  Applying  eq.  (67)  suc- 
cessively to  each  pair  of  segments,  we  obtain'  n  —  1  equations 
of  the  first  degree  with  respect  to  these  quantities,  which 
by  successive  eliminations  give  us  the  values  of  the  moments, 
M,,  M,,  .....  Mn. 

These  equations  will  be  of  the  following  form  : 

2  ft  +  y  M,  +  Z,M,  =  i  fay  +  wjf) 
a  ft  +  Z.)  M,  +  Z,M.  =  i  (w,l,>  +  w,l*) 

*##### 
!  +  2  4.!  + 


From  these  equations,  the  reactions  at  the  points  of  sup 
port  can  be  determined,  and  knowing  all  the  external  forces 
the  strains  on  the  beam  may  be  calculated. 


TORSION.  125 

TORSION. 

195.  A  beam  strained  by  a  system  of  ext/aneous  forces, 
among  which  is  a  couple  acting  in  a  plane  perpendicular  to 
the  axis  of  the  piece,  will  be  subjected  to  a  stress  of  torsion 
in  addition  to  the  other  stresses  already  described. 

Suppose  a  beam  fixed  at  one  end  (Fig.  30)  and  a  couple 
applied  to  the  free  end,  F,  the  axis  of  the  couple  intersecting 
the  axis  of  the  piece,  and  the  plane  of  the  couple  perpen- 
dicular to  the  axis.  The  action  of  the  couple  will  be  to 
twist  the  beam  around  its  axis,  causing  a  twisting  strain  of 
the  fibres  and  developing  torsional  stresses  in  the  material. 


FIG.  30.  FIG.  31. 

To  determine  the  stress  of  torsion  at  any  cross-section  as 
C  D,  let  a  be  equal  to  the  angular  amount  of  torsion  between 
any  two  cross-sections  of  the  beam,  and  ft  the  amount  of 
angular  change  for  a  unit  of  length. 

It  is  assumed  that  the  total  amount  of  angular  change  of 
any  fibre  between  any  two  sections,  or  a,  is  directly  propor- 
tional to  the  distance  between  the  sections,  and  that  the 
stress  of  torsion  developed  in  the  fibre  is  directly  proportional 
to  its  distance  from  the  axis  of  the  piece. 

Let  T/  =  the  stress  of  torsion  in  any  fibre,  a  =  the  area 
of  cross-section  of  the  fibre,  and  G  =  the  coefficient  of  tor- 
sional elasticity;  then 

-S  =  G&     or    T',  =  aGft. 

Let  0  be  taken  as  the  pole.  (Fig.  31)  0  Z,  the  fixed  line, 
and  r  and  v  the  polar  co-ordinates  of  points  in  the  plane  of 
cross-section  C  D.  Then 

a  =  rdr  dv. 

Since  the  stress  is  assumed  to  be  directly  proportional  to 
the  distance  of  the  fibre  from  the  axis,  we  get  by  substitut- 


126  CIVIL  ENGINEERING. 

ing  for  a  its  value,  and  multiplying  byr,  the  intensity  of 
the  stress  in  the  fibre  at  the  distance  r  from  the  axis  to  he 

G  ft  i*dr  dv. 

Suppose  the  section  C  D  to  be  fixed.  The  twisting  action 
of  the  couple  at  F  is  transmitted  from  section  to  section  of 
the  piece  until  it  reaches  C  D,  where  it  is  opposed  by  the 
resistance  developed  in  the  section.  The  moment  of  resist- 
ance offered  by  the  fibre  at  the  distance  r  from  the  axis  will 
be  the  intensity  of  the  twisting  stress  in  the  fibre  multiplied 
by  its  lever  arm,  r,  or 

G  ft  rzdr  dv. 

The  total  moment  of  the  resistance  developed  in  the  cross- 
section  C  D  may  be  expressed  as  follows : 


drdv,  .    .    .     .     (74) 

Eepresent  the  moment  of  the  couple  acting  at  the  section 
F  by  F'  x  A,  and  equating  the  moments,  we^have 

v  =  W\,      .    .    (75) 

This  expression  /   /  r*drdv  is  called  the  polar  moment 

of  inertia  ;  that  is,  the  moment  of  inertia  of  a  cross-section 
of  the  beam  about  an  axis  through  its  centre  and  perpendicu- 
lar to  the  plane  of  cross-section. 
Representing  it  by  lp,  we  have 

G/SI^F'A,      ....    (76) 

Suppose  the  cross-section  considered  to  be  a  circle,  whose 
radius  ==  R,  and  the  section  in  which  the  resistance  is  con- 
sidered is  at  the  distance  I  from  the  plane  of  the  twisting 
couple.  Equation  (76)  would  become  for  this  case,  by 

substituting  1L  for  ft,  and  J  ;rR4  for  1^ 


TORSION.  127 

196.  General  Morin,  in  his  work  on  Strength  of  Materials, 
gives  the  value  for  G  for  different  materials. 

The  following  are  some  of  the  values  : 

Wrought  iron  .............  G  =    8,533,700  Ibs. 

Cast-iron  ..................  G  =     2,845,000  Ibs. 

Cast-steel  ..................  G  =  14,223,000  Ibs. 

Copper  ....................  G  =    6,210,000  Ibs. 

Oak  .......................  G  =       569,0001bs. 

Pine  ......................  G  =       616,000  Ibs. 

Rupture  by  Twisting. 

197.  It  is  assumed  that  the  torsional  stress  developed  in 
the  fibres  of  a  piece  varies  directly  with  the  distance  of  the 
fibre  from  the  axis  of  torsion,  and  is  greatest  in  the  fibres 
farthest  from  this  axis.     If   the  strain  be  increased   until 
rupture  takes  place,  those  fibres  farthest  from  the  axis  will 
be  the  ones  to  give  way  first. 

The  intensity  of  the  torsional  stress  for  any  cross-section 
developed  in  a  fibre  at  the  distance  r  from  the  axis  is 

G  ft  r*dr  dv. 

This  expression  divided  by  the  area  of  cross-section  of  the 
fibre,  r  dr  dv,  gives  G  ft  r  as  the  intensity  of  the  torsional 
stress  on  the  unit  of  surface  at  the  distance  r  from  the  axis. 
Represent  this  intensity  by  T',  and  we  have 

T  =  Grftr. 

Multiplying  both  members  of  this  equation  by  Ip,  and  di- 
viding by  r,  we  get 


in  which  the  second  member  is  the  same  as  the  first  member 
of  equation  (76).    Hence, 

—  Ip  =F'A 
r 

from  which  we  get 

T  =  ?*r,        .        .,".      .        (78) 

iP, 

or,  an  expression  for  the  torsional  stress  on  any  unit  of  cross- 
section  of  a  piece  strained  by  a  twisting  force. 


128  CIVIL   ENGINEERING. 

Let  d  =  the  greatest  value  that.?*  can  have  for  any  cross- 
section.  If  d  be  substituted  for  r  in  equation  (78)  the  result- 
ing value  of  T"  will  be  the  stress  on  the  unh  farthest  from 
the  axis  for  the  cross-section  considered. 

Suppose  F'A  to  be  increased  until  rupture  is  produced, 
then  T'  for  this  value  of  r  —  d,  in  the  section  where  rupture 
begins,  will  be  T^,  the  modulus  of  torsion,  or 

TV,  =  F'A  x  ~ (79) 

*p 

from  which  the  values  of  the  modulus  of  torsion  may  be  de- 
duced. 

INFLUENCE  OF  TEMPERATURE. 

198.  The  influence  of  changes  in  temperature,  especially 
in  the  metals,  forms  an  important  element  to  be  considered 
in  determining  the  amount  of  strain  on  a  beam. 

If  the  beam  is  free  to  move  at  both  ends,  there  will  be  no 
strain  in  the  beam  arising  from  the  changes  of  temperature  ; 
if  the  ends  are  fixed,  there  will  be,  and  these  strains  must  be 
determined. 

The  elongation  or  contraction  produced  by  the  changes  of 
temperature  is  known  for  the  different  metals.  The  amount 
of  strain  upon  the  unit  of  area  will  be  the  same  as  that  pro- 
duced by  a  force  elongating  or  contracting  the  beam  an 
amount  equal  to  that  resulting  from  the  change  of  tempera- 
ture under  consideration. 


CHAPTEK  YII. 

STRENGTH  OF  BEAMS. 

PROBLEMS. 

199.  The  object  of  the  previous  discussions  has  been  to  find 
the  strains  to  which  a  beam  is  subjected  by  certain  known 
forces  applied  to  it. 

The  problems  which  now  follow  are: 

Knowing  all  the  external  forces  acting  on  a  beam,  to  de- 
tennwe  the  form  and  dimensions  of  its  cross-section,  so  that 


STRENGTH    OF   BEAMS.  129 

the  strain  on  the  unit  of  surf  ace  shall  at  no  point  be  greater 
than  the  limit  allowed ;  and  knowing  the  form  and  dimen- 
sions of  the  cross-section  of  a  beam,  to  determine  tJie  load 
which  it  will  safely  bear. 

There  are  two  cases  ;  one  is  where  the  cross- section  is  con- 
stant throughout  the  beam  ;  and  the  other  is  where  it  varies 
from  one  point  to  another. 

1st  CASE.— BEAMS  OF  UNIFORM  CROSS-SECTION. 

200.  Strength  of  beam  strained  by  a  tensile  force. 
Let  W  be  the  resultant  force  whose  line  of  direction  is  in 
the  axis  of  the  beam  and  whose  action  is  to  elongate  it. 

From  the  equation  preceding  eq.  (5),  we  have 

W 

—  =  the  stress  on  a  unit  01  cross-section. 
A 

Knowing  the  value  of  T  for  different  materials,  a  value  less 
than  T  for  the  given  material  is  assumed  for  the  stress  to  be 
allowed  on  the  unit  of  cross-section.  Assuming  this  value  of 
the  stress  and  calling  it  T1?  we  have 

W 

A  =  -.     ..,.*.     (80) 

From  which,  knowing  the  form  of  cross-section  and  its  area, 
the  problem  can  be  solved. 

Suppose  the  form  to  be  rectangular,  and  let  b  be  the 
breadth  and  d  the  depth.  Then 

W 

A  =  b  x  d,  or  bd  =  — ; 
J-i 

in  which,  if  •  b  be  assumed,  d  can  be  determined,  and  the  con- 
verse. 

The  solution  of  the  reverse  problem  is  evident.  Knowing 
A  and  T1?  the  value  of  W,  or  the  load  which  will  not  produce 
a  stress  greater  than  TL  on  the  unit  of  area,  is  easily  deter- 
mined. 

201.  Strength  -when  strained  by  a  compressive  force. 
For  all  practical  purposes,  it  is  assumed  sufficiently  exact 

for  short  pieces  to  apply  the  methods  just  given  for  tension, 
substituting  Ct  for  Tt ;  the  former  being  the  assumed  limit  of 
compressive  stress  on  the  unit  of  area.  "When  the  pieces  are 
longer  than  five  times  their  diameter,  they  bend  under  the 
crushing  load  and  break  by  bending,  or  by  bending  and 
by  crushing. 
9 


130 


CIVIL   ENGINEERING. 


Rankine  gives  the  following  limits  of  proportion  between 
length  and  diameter,  within  which  failure  by  crushing  alone 
will  take  place,  and  beyond  which  there  is  a  sensible  ten- 
dency to  give  way  by  bending  sideways. 

Pillars,  rods,  and  struts  of  cast  iron,  in  which  the  length 
is  not  more  than  five  times  the  diameter. 

The  same  of  wrought  iron,  not  more  than  ten  times  the 
diameter. 

The  same  of  dry  timber,  not  more  than  twenty  times  the 
diameter. 

202.  Formulas  for  obtaining  the  strength  of  columns 
or  pillars  'whose  lengths  are  greater  than  five  times  the 
diameter  of  cross-section,  when  subjected  to  a  compres- 
sive  strain. 

The  formulas  deduced  by  Mr.'  Hodgkinson,  from  a  long  series 
of  experiments  made  upon  pillars  of  wood,  wrought  iron,  and 
cast  iron  are  much  used  in  calculating  the  strength  of  pillara 
or  columns  strained  by  a  force  of  compression. 

Hodgldnsorfs  Formulas. 

Table  for  finding  the  strength  of  pillars,  in  which 
W  =  the  breaking  weight,  in  tons  of  2,000  pounds ; 
L  =  the  length  of  the  column  in  feet ; 
D  =  the  diameter  of  exterior  in  inches ; 
d  =  the  diameter  of  interior  in  inches. 


Nature  of  column. 


Both  ends  being  round- 
ed, length  of  column 
exceeding  15  times 
its  diameter. 


Both  ends  being  flat, 
the  length  of  column 
exceeding  30  times 
its  diameter. 


Solid  square  pillar  of 
red  cedar  (dry).  .  , 

Same  of  oak  (Dantzic) 
dry , 

Solid  cylindrical  col.  of 
wrought  iron .... 


Solid  cylindrical  col.  of 
cast  iron  . 


Hollow  cylindrical  col. 
of  cast  iron . 


W  = 

W  =  16.6^ 

W  =  U.l 


W  =  12.2^ 


!•»'* 


W  =49.6^ 


STRENGTH    OF   PILLARS. 


131 


If  the  column  be  shorter  than  that  given  in  the  table,  and 
more  than  five  times  its  diameter,  the  strength  may  be  deter- 
mined by  the  following  formula : 


WAG 


.    .    .    .    (81) 


in   which  W=  the  breaking   weight,  computed  from   the 
formulas  in  the  above  table ; 

C  =  the  modulus  of  crushing  in  tons ; 

A  =  the  cross-section  in  square  inches ;  and 

W  =  the  strength  of  the  column  in  tons. 


Gordons  Formulas. 

These  are  deduced  from  the  same  experiments,  and  are  aa 
follows : 


SOLID  PILLARS. 


Cross-section  a  square. 


Of  cast  iron  W  = 


80,000  A 


Of  wrought  iron      .    .    W  = 

1  + 


266  52 
36,000  A 


.  (82) 


HOLLOW  PILLARS. 
Circular  in  cross-section. 


Of  cast  iron    ,          .    .     W  = 


Of  wrought  iron      .    .     W  = 


80,000  A  1 


.     .  (83) 


132 


CIVIL  ENGINEERING. 


Cross-section  a  square. 
Of  cast  iron   .    .    . 


Of  wrought  iron 


_  80,000  A 


1  + 


533  62 


_  36,000  A 


•     •  (**) 


6,000  I 
in  which, 

"W  =  the  breaking  load  in  pounds ; 
A  =  the  area  of  cross-section  in  square  inches ; 
I  —  the  length  of  the  pillar  in  inches ; 
b  =  the  length  of  one  side  of  the  cross-section ;  and 
d  =  the  diameter  of  the  outer  circumference  of  the  base. 
These  formulas  apply  to  pillars  with  flat  ends,  the  ends 
being  secured  so  that  they  cannot  move  laterally  and  the  load 
uniformly  distributed  over  the  end  surface.     In  the  hollow 
columns,  the  thickness  of  the  metal  must  not  exceed  \  of  the 
outer  diameter. 


Mr.  G.  Shaler  Smith? s  Formula. 

This  formula  is  deduced  from  experiments  made  by  Mr. 
Smith  on  pillars  of  both  white  and  yellow  pine,  and  is 


/== 


.     .     .     (85) 


in  which  5  and  I  are  in  inches,  and  represent  the  same  quanti- 
ties as  in  the  preceding  formulas.  W  is  the  breaking  load 
on  the  square  inch  of  cross-section  in  pounds. 

203.  Mr.  Hodgkinson,  in  summing  up  his  conclusions  de- 
rived from  the  experiments  made  by  him  on  the  strength  of 
pillars,  stated  that : 

"  1st.  In  all  long  pillars  of  the  same  dimensions,  the  resist- 
ance to  crushing  by  flexure  is  about  three  times  greater  when 
the  ends  of  the  pillars  are  flat  than  when  they  are  rounded. 

"  2d.  The  strength  of  a  pillar,  with  one  end  rounded  and 
the  other  flat,  is  the  arithmetical  mean  between  that  of  a 
pillar  of  the  same  dimensions  with  both  ends  round,  and  one 
with  both  ends  flat.  Thus  of  three  -cylindrical  pillars,  all  of 
the  same  length  and  diameter,  the  first  having  both  its  euda 


STRENGTH   OF   PILLARS.  133 

rounded,  the  second  with  one  end  rounded  and  one  flat,  and 
the  third  with  both  ends  flat,  the  strengths  are  as  1,  2,  3, 
nearly. 

"  3d.  A  long,  uniform,  cast-iron  pillar,  with  its  ends  firmly 
fixed,  whether  by  means  of  disks  or  otherwise,  has  the  same 
power  to  resist  breaking  as  a  pillar  of  the  same  diameter,  and 
half  the  length,  with  the  ends  rounded  or  turned  so  that  the 
force  would  pass  through  the  axis. 

"  4th.  The  experiments  show  that  some  additional  strength 
is  given  to  a  pillar  by  enlarging  its  diameter  in  the  middle 
part ;  this  increase  does  not,  however,  appear  to  be  more  than 
one-seventh  or  one-eighth  of  the  breaking  weight." 

Similar  pillars.—"  In  similar  pillars,  or  those  whose  length 
is  to  the  diameter  in  a  constant  proportion,  the  strength  is 
nearly  as  the  square  of  the  diameter,  or  of  any  other  linear 
dimension ;  or,  in  other  words,  the  strength  is  nearly  as  the 
area  of  the  transverse  section. 

"  In  hollow  pillars,  of  greater  diameter  at  one  end  than  the 
other,  or  in  the  middle  than  at  the  ends,  it  was  not  found  that 
any  additional  strength  was  obtained  over  that  of  cylindrical 
pillars. 

"  The  strength  of  a  pillar,  in  the  form  of  the  connecting 
rod  of  a  steam-engine "  (that  is,  the  transverse  section  pre- 
senting the  figure  of  a  cross  +),  "was  found  to  be  very 
small,  perhaps  not  half  the  strength  that  the  same  metal 
would  have  given  if  cast  in  the  form  of  a  uniform  hollow 
cylinder. 

"  A  pillar  irregularly  fixed,  so  that  the  pressure  would  be 
in  the  direction  of  the  diagonal,  is  reduced  to  one-third  of  its 
strength.  Pillars  fixed  at  one  end  and  movable  at  the  other, 
us  in  those  flat  at  one  end  and  rounded  at  the  other,  break  at 
one- third  the  length  from  the  movable  end ;  therefore,  to 
economize  the  metal,  they  should  be  rendered  stronger  there 
than  in  other  parts. 

"  Of  rectangular  pillars  of  timber,  it  was  proved  experimen- 
tally that  the  pillar  of  greatest  strength  of  the  same  material 
is  a  square." 

Long-continued  pressure  on  pillars. — "To  determine 
the  effect  of  a  load  lying  constantly  on  a  pillar,  Mr.  Fairbairn 
had,  at  the  writer's  suggestion,  four  pillars  cast,  all  of  the 
same  length  and  diameter.  The  first  was  loaded  with  4  cwt., 
the  second  with  7  cwt,  the  third  with  10  cwt.,  and  the  fourth 
with  13  cwt. ;  this  last  load  was  ^  of  what  had  previously 
broken  a  pillar  of  the  same  dimensions,  when  the  weight  waa 
carefully  laid  on  without  loss  of  time.  The  pillar  loaded 


134  CIVIL  ENGINEERING. 

with  13  cwt.  bore  the  weight  between  five  and  six  months, 
and  then  broke." 

STRENGTH  OF  BEAM  TO   RESIST  A   SHEARING   FORCE. 

204.  It  has  been  shown  that  the  transverse  shearing  stress 
varies  directly  with  the  area  of  cross-section,  and  that  we  have 

S'  =  AS, 

in  which  S  is  the  modulus  of  shearing.  Assuming  a  value 
which  we  represent  by  Si  less  than  S  for  the  given  material, 
and  we  have 

W  =  ASt, 

in  which  "W"  is  the  force  producing  shearing  strain  and  B!  the 
limit  of  the  shearing  stress  allowed  on  the  unit  of  surface. 
Knowing  the  form,  the  dimensions  to  give  the  cross-section 
for  any  assumed  stress  are  easily  obtained. 

TRANSVERSE    STRENGTH    OF   BEAMS. 

205.  The  stress  on  the  unit  of  area  of  the  fibres  of  a  beam 
at  the  distance  y  from  the  neutral  axis,  in  the  case  of  trans- 
verse strain,  is  obtained  from  eq.  (21), 

y  ' 

As  previously  stated,  the  hypothesis  is  that  the  stress  on 
the  unit  of  area  increases  as  y  increases,  and  will  be  greatest 
in  any  section  when  y  has  its  greatest  value.  That  unit  of 
area  in  the  section  farthest  from  the  neutral  axis  will  there* 
fore  be  the  one  that  has  the  greatest  stress  upon  it.  Now 
suppose  M  to  be  increased  gradually  and  continually.  It 
will  at  length  become  so  great  as  to  overcome  the  resistance 
of  the  fibres  and  produce  rupture.  Since  the  material  is 
homogeneous,  and  supposed  to  resist  equally  well  both  ten- 
sion and  compression,  the  stresses  on  the  unit  of  area  at  the 
same  distance  on  opposite  sides  of  the  neutral  surface  are 
considered  equal. 

Representing  by  R  the  stress  on  the  unit  of  area  farthest 
from  the  neutral  surface  in  the  section  where  rupture  takes 
place,  and  the  corresponding  value  of  y  by  y\  we  have 

5J=M',    .    .    .    .    (86) 

in  which  M'  is  the  bending  moment  necessary  to  produce 
rupture  at  this  section. 


TRANSVERSE   STRENGTH   OF   BEAMS.  135 

When  the  cross-section  is  a  rectangle,  in  which  I  is  the 
breadth  and  d  the  depth,  I  is  equal  to  T*ybd*,  and  the  greatest 

value  of  y'is  r-  ;  substituting  these  values  in  eq.  (86)  we  have 
for  a  beam  with  rectangular  cross-section, 


K  x  4&P=M'.  .....     (87) 

The  first  member  is  called  the  moment  of  rupture  and 
its  value  for  different  materials  has  been  determined  by  ex- 
periment. 

These  experiments  have  been  made  by  taking  beams  of 
known  dimensions,  resting  on  two  points  of  support,  and 
breaking  them  by  placing  weights  at  the  middle  point. 

From  equation  (87)  we  have 

M/  ' 


in  which,  substituting  the  known  quantities  from  the  exper- 
iment, the  value  of  fi,  called  the  modulus  of  rupture,  is 
obtained. 

These  values,  thus  obtained,  are  especially  applicable  to  all 
beams  with  a  rectangular  cross-section,  and  with  sections  that 
do  not  differ  materially  from  a  rectangle.  "Wliere  other 
cross  sections  are  used,  special  experiments  must  be  made. 

206.  In  a  beam  of  uniform  cross-section  the  stresses  on  the 
different  sections  vary,  and  that  particular  section  at  which 
the  moment  of  the  external  forces  is  the  greatest  is  the  one 
where  rupture  begins,  if  the  beam  break.  This  section  most 
liable  to  break  may  be  called  the  dangerous  section. 

In  rectangular  beams  the  dangerous  section  will  be  where 
the  moments  of  the  straining  forces  are  the  greatest. 

Let  "W  denote  the  total  load  on  a  beam,  and  I  its  length,  we 
have  for  the  greatest  moments  in  the  following  cases  : 

M  =  WZ,  when  the  load  is  placed  at  one  end  of  a  beam,  and 
the  other  end  fixed. 

M=—  x  I  =  4"W7,  for  the  same  beam  uniformly  loaded. 
2 
•^y       ^ 

M  =  —  x  ~  JWZ,  when  the  load  is  placed  at  the  middle 

2        2 

point  of  a  beam  resting  its  extremities  on  supports. 
M  =  —  x  J  ^  =  £WZ,  for  the  same  beam  uniformly  loaded. 


If  a  less  value  than  that  necessary  to  break  the  beam  be 


136  CIVIL  ENGINEERING. 

substituted  in  eq.  (88)  for  M',  the  corresponding  value  for  R, 
will  not  be  that  for  the  modulus  of  rupture,  but  will  merely 
be  the  stress  on  the  unit  of  area  farthest  from  the  neutral 
axis  in  the  dangerous  section.  Suppose  a  beam  strained  by  a 
force  less  than  that  which  will  produce  ru-pture  and  find  for 
M  the  corresponding  maximum  value  for  each  case.  Sub- 
stituting these  in  eq.  (87),  we  have 


(89) 


in  which  E'  is  the  greatest  stress  on  the  unit  of  area  in  the 
dangerous  section  for  the  corresponding  case  x>f  rectangular 
beams,  whose  moments  are  given  above. 

The  value  of  R  for  a  material  may  be  determined  by  find- 
ing the  force  that  will  break  a  piece  of  the  same  material, 
of  a  similar  form,  and  substituting  the  moment  of  this 
force  for  M'  in  eq.  (86),  and  deducing  the  value  of  R. 

Some  of  the  values  of  R  for  pieces  of  rectangular  cross- 
section  are  as  follows  : 

Material.  Value  of  R. 

Ash  ..............................  12,156  Ibs. 

Chestnut  ..........................  10,660    " 

Oak  ...............................  10,590   " 

Pine  ............  .  .  .  ...............      8,946   « 

Fir  ...............................      6,600   " 

Cast-iron  ..........................  33,000    " 

The  value  of  R  is  also  taken  as  equal  to  eighteen  times  the 
force  required  to  break  a  piece  of  one  inch  cross-section,  rest- 
ing on  two  supports  one  foot  apart,  and  loaded  at  the  middle. 

207.  From  the  definition  for  R,  it  would  seem,  as  before 
stated,  that  it  should  be  equal  either  to  C  or  to  T,  depending 
upon  whether  the  beam  broke  by  crushing  or  tearing  of  the 
fibres.  In  fact,  it  is  equal  to  neither,  being  generally  greater 
than  the  smaller  and  less  than  the  greater  ;  as  shown  in  the 
case  for  cast  iron,  for  which 

The  mean  value  of  C  =  96,000  pounds  ; 
The  mean  value  of  T  =  16,000  pounds  ;  and 
The  mean  value  of  R  =  36,000  pounds. 


If,  ther,  instead  of  taking  R  from  the  tables,  the  value  of  T 

e  calcu- 
That is, 


,       r,   na    o     ang        rom     e   aes,     e  v 
or  C  6e  used,  taking  the  smaller  value  of  the  two,  the  calcu- 
lated ^reiigth  of  the  beam  will  be  on  the  safe  side. 


INFLUENCE   OF   CROSS-SECTION.  137 

the  strength  of  the  beam  will  be  greater  than  that  found  by 
calculation. 

Experiments  should  be  made  upon  the  materials  to  be  used 
in  any  important  structure,  to  find  the  proper  value  for  R. 

In  determining  the  safe  load  to  be  placed  on  a  beam,  the 
following  values  for  R'  may  be  taken  as  a  fair  average : 

For  seasoned  timber,  R'  =  850  to  1,200  pounds ; 

For  cast  iron,  R'  =  6,000  to  8,000  pounds ; 

For  wrought  iron,  R'  =  10,000  to  15,000  pounds. 


INFLUENCE  OF  THE  FORM  OF  CROSS  SECTION  ON  THE  STRENGTH 

OF  BEAMS. 

208.  The  resistance  to  shearing  and  tensile  strains  in  any 
section  of  a  beam  is  the  same  for  each  unit  of  surface  through- 
out the  section.  The  same  has  been  assumed  for  the  resist- 
ance to  compressive  strains  within  certain  limits.  Hence  so 
long  as  the  area  of  cross-section  contains  the  same  number  of 
superficial  units,  the  form  has  no  influence  on  the  resistance 
offered  to  these  strains. 

This  is  different  in  the  case  of  a  transverse  strain. 

We  may  write  equation  (21)  under  this  form, 


In  this,  if  we  suppose  M  to  have  a  constant  value,  P  will  then 

y 

vary  directly  with  the  factor  ^;  that  is,  as  this  factor  increases 

or  decreases,  there  will  be  a  corresponding  increase  or  decrease 
in  P. 

Represent  by  d  the  depth  of  the  beam,  \d  will  be  the 
greatest  value  that  y  can  have.  It  is  readily  seen,  that  for 
any  increase  of  %dy  I  will  increase  in  such  a  proportion  as  to 

decrease  the  value  of  —  ,  and  hence  decrease  the  amount  of 

stress  on  the  unit  of  area  farthest  from  the  neutral  axis. 
Therefore  we  conclude  that  for  two  sections  having  the  same 
area,  the  stress  on  the  unit  of  surface  farthest  from  the  neutral 

d 
axis  is  less  for  the  one  in  which  ^  is  the  greater. 

This  principle  affords  a  means  of  comparing  the  relative 
resistances  offered  to  a  transverse  strain  by  beams  whose  cross- 
sections  are  different  in  form  but  equivalent  in  area. 


138  CIVIL   ENGINEERING. 

For  example,  compare  the  resistances  offered  tc  a  trans- 
verse strain  by  rectangular,  elliptical,  and  I-girders,  with 
equivalent  cross-sections. 

The  values  of  I  for  the  rectangle,  ellipse,  and  I-section  are 
respectively, 

I  =  ^&p,  I  =  frirlffi,  and  I  =  T\(bd?  -  Vd'*\ 

Represent  the  equivalent  cross-section  by  A,  and  we  will 
have  A  =  M  for  the  rectangle,  A  =  \Trbd  for  the  ellipse,  and 
A  =  b(d—d')  for  the  I-section.  The  latter  is  obtained  by 
neglecting  the  breadth  of  the  rib  joining  the  two  flanges,  its 
area  being  small  compared  with  the  total  area,  and  by  regard- 
ing dz=  dd  =  d'2,  d  —  d  being  small  compared  with  d. 

Substituting  these  values  of  A  in  the  factor  !=-,  we  get  for 

the  rectangle,  -r—  .  ;  for  the  ellipse,  -r—^  ;  for  the  I-section  —  —  •,. 
A.d  J\.d  Act/ 

Id 
Hence  we  see  that  —  -  is  least  for  the  third,  and  greatest  for 

the  second,  and  therefore  conclude  that  the  stress  on  the 
unit  of  surface  farthest  from  the  neutral  axis  is  the  least  for 
the  I-girder,  and  its  resistance  to  a  transverse  strain  is  greater 
than  either  of  the  other  two  forms. 

Since  the  quantity  A  contains  b  and  d,  by  decreasing  5  and 
increasing  <#,  within  limits,  the  resistance  of  any  particular 
form  will  be  increased.  And  hence,  in  general,  the  mass  of 
fibres  should  be  thrown  as  far  from  the  neutral  axis  as  the 
limits  of  practice  will  allow. 

The  strongest  Beam  that  can  be  cut  out  of  a  Cylin- 
drical Piece. 

209.  It  is  oftentimes  required  to  cut  a  rectangular  beam 
out  of  a  piece  of  round  timber.  The  problem  is  to  obtain  the 
one  of  greatest  strength. 

Denote  by  D  the  diameter  of  the  log,  by  1}  the  breadth, 
and  d  the  depth  of  the  required  beam. 

From  the  value 

R'-    M 
" 


it  is  evident  tHat  the  strongest  beam  is  the  one  in  which  M* 
has  its  maximum  value. 


BEAMS    OF   UNIFORM   STRENGTH.  13!) 

Representing  the  crosstsection  of  the  beam  and  of  the  log 
by  a  rectangle  inscribed  in  a  circle,  we  have 


D  being  the  diameter  of  the  circle.    Multiplying  by  5,  gives 
Iff  =  5D2-  P. 

In  order  to  have  bd?  a  maximum,  D2—  35s  must  be  equal  te 
zero,  which  gives 


and  this,  substituted  in  the  expression  for  d2,  gives 


To  construct  this  value  of  5,  draw  a  diameter  of  the  circle, 
and  from  either  extremity  lay  off  a  distance  equal  to  one- 
*hird  of  its  length.  At  this  point  erect  a  perpendicular  to 
she  diameter,  and  from  the  point  where  it  intersects  the  cir- 
cumference draw  the  chords  joining  it  with  the  ends  of  the 
diameter.  These  chords  will  be  the  sides  of  the  rectangle. 

2d  CASE.—  BEAMS  OF  VARIABLE  CROSS-SECTION. 

210.  Beams  of  uniform  strength.  —  Beams  which  vary 
in  size  so  that  the  greatest  stress  on  the  unit  of  area  in  each 
section  shall  be  constant  throughout  the  beam,  form  the  prin- 
cipal class  of  this  second  case. 

In  the  previous  discussions  and  problems  the  bar  or  beam 
has,  with  but  one  exception,  been  considered  as  having  a 
uniform  cross-section  throughout,  and  in  th6se  discussions  the 
moment  of  inertia,  I,  has  been  treated  as  a  constant  quantity. 

Since  the  beams  had  a  uniform  cross-section  it  is  evident 
that  the  greatest  stress  was  where  the  moment  of  the  exter- 
nal forces  was  the  greatest. 

Finding  this  greatest  moment  of  the  external  forces,  we 
determined  the  greatest  stress  and  the  section  at  which  it 
acted.  If  this  section  was  strong  enough  to  resist  this  action, 
it  follows  that  all  other  sections  were  strained  less  and  were 
larger  than  necessary  to  resist  the  stresses  to  which  they 
were  exposed  ;  in  other  words,  there  was  a  waste  of  material. 

The  greatest  stress  on  a  unit  of  surface  of  cross-section 
being  known  or  assumed,  let  us  impose  the  condition  that  it 
shall  be  the  same  for  every  section  of  the  beam.  This  will 


140  CIVIL   ENGINEERING. 

necessitate  variations  in  the  cross-sections,  hence  I  will  vary 
and  must  be  determined  for  each  particular  case. 

A  beam  is  called  a  "  solid  of  equal  resistance  "  when  so 
proportioned  that,  acted  on  bj  a  given  system  of  external 
forces,  the  greatest  stresses  on  the  unit  of  area  are  equal  for 
every  section. 

This  subject  was  partly  discussed  under  the  head  of  tension 
in  determining  the  form  of  a  bar  of  uniform  strength  to  resist 
elongation.  The  method  there  used  could  be  applied  to  the 
case'of  a  beam  to  resist  compression. 

Beams  of  Uniform  Strength  to  resist  a  Transverse 

Strain. 

211.  Suppose  the  beam  to  be  acted  upon  by  a  force  produc- 
ing a  transverse  strain,  and  let  the  cross-section  be  rectangular. 

Let  b  and  d  represent  the  breadth  and  depth  of  the  beam, 
and  we  have 

I  =  jytxP. 

Substituting  in  eq.  (21)  this  value  of  I,  and  giving  to  y  its 
greatest  value,  which  is  -J<#,  we  have 


or 


for  the  stress  on  a  unit  of  surface  at  the  distance  \d  from  the 
neutral  axis  in  the  cross-section  under  consideration. 

The  greatest  stress  will  be  found  in  that  section  for  which 
M  is  the  greatest.  Kepresenting  this  moment  by  M"  and  the 
corresponding  value  of  P'  for  this  section  by  P",  we  have 

"M  " 

P"  — 

~ 


This  value  of  P"  is  then  the  greatest  value  of  the  stress, 
upon  the  unit  of  surface,  produced  by  the  deflecting  forces 
acting  to  bend  the  beam. 

From  the  conditions  of  the  problem,  the  greatest  stress  on 
the  unit  of  surface  must  be  the  same  for  every  cross-section. 
Eq.  (90)  gives  the  greatest  stress  on  the  unit  of  surface  in  any 
cross-section.  It  therefore  follows  that  for  a  rectangular  beam 
of  uniform  strength  to  resist  a  cross-strain,  we  must  have 


BEAMS   OF   UNIFOEM   STRENGTH. 


141 


Since  P"  is  constant,  b  or  d,  or  both  of  them,  must  vary  as 
M  varies,  to  make  the  equation  a  true  one ;  that  is,  the  area  of 
cross-section  must  vary  as  M  varies. 

We  may  assume  b  constant  for  a  given  case,  and  giving 
different  values  to  M,  deduce  the  corresponding  ones  for  d ; 
or,  assuming  d  constant,  do  the  same  for  b ;  or  we  may  assume 
that  their  ratio  shall  be  constant. 

For  the  first  case,  b,  the  breadth  constant,  we  have 


(93) 


For  the  second  case,  d,  the  depth  constant,  we  have 

M 

and  for  the  third,  their  ratio  constant,  b  =  rd,  we  have 


The  assumed  values  of  M  with  the  deduced  values  of  dt 
from  eq.  (93),  will  show  the  kind  of  line  cut  out  of  the  beam 
by  a  vertical  section  through  the  axis,  when  the  breadth  is 
constant ;  and  the  deduced  values  of  £,  from  eq.  (94),  will 
show  the  kind  of  line  cut  out  of  the  beam  by  a  horizontal 
section  through  the  axis  when  the  depth  is  constant.  These 
lines  will  show  the  law  by  which  the  sections  vary  from  one 
point  to  another  throughout  the  beam, 

As  examples  take  the  following  cases : 

212.  CASE  IST. — A  horizontal  beam  ftrmly  fastened  at  one 


FIG.  32. 


end  (Fig.  32),  and  the  other  end  free  to  move,  strained  by  a 
load  uniformly  distributed  along  the  line,  A  B. 


142 


CIVIL  ENGINEERING. 


Take  B  as  the  origin  of  co-ordinates,  B  A  the  axis  of  X,  y 
positive  downwards,  the  axis  of  Z  horizontal,  and  w  the  weight 
on  a  unit  of  length. 

The  moment  of  the  weight  acting  at  any  section  as  D  is 

-~-f  substituting  which  for   M  in  the  expression  (93)  for  d, 
we  have 


which  is  the  equation  of  a  right  line  as  B  D,  passing  through 
the  origin  of  co-ordinates. 

If  the  depth  be  constant,  the  breadth  will  vary  from  point 
to  point,  and  the  different  values  of  the  ordinate  may  be  ob- 
tained by  substituting  this  moment  for  M  in  expression  (94), 
and  we  have 


3w 


0  =  Z  = 


which  is  the  equation  of  a  parabola  having  its  vertex  at  B, 
as  in  Fig.  33. 


FIG.  33. 


213.  CASE  2D.  —  A  beam  as  in  preceding  case  strained  by  a 
load,  W,  concentrated  and  acting  at  -#,  the  weight  of  the 
learn  disregarded. 

The  breadth  being  constant,  we  have 


or 


6W 


BEAMS    OF  UNIFORM    STRENGTH. 


143 


which  is  the  equation  of  a  parabola,  the  vertex  of  which  is 
at  B.    (Fig.  34) 


FIG.  34. 

Suppose  the  depth  constant  ;  in  this  case  we  have 

6W 


which  is  the  equation  of  a  right  line,  and  shows  that  the  plan 
of  the  beam  is  triangular. 

214.  CASE  3o.  —  /Suppose  the  beam  resting  on  two  supports 
at  its  ends  and-  uniformly  loaded. 

Kepresent  by  2Z  the  distance  between  the  supports,  by  w 
the  load  on  a  unit  of  length,  and  take  A  (Fig.  22)  as  the  origin 
of  co-ordinates. 

The  moment  of  the  external  forces  at  any  section,  as  D, 
will  be  tyotf'  —wlx,  which  substituted  in  eq.  (93),  gives 


TO  o 

=       *- 


which  is  the  equation  of  an  ellipse. 

This  moment  substituted  in  eq.  (94),  gives 


,  _ 
~ 


« 
~ 


which  is  the  equation  of  a  parabola. 

215.  In  a  similar  way  we  may  determine  the  forms  of  beams 
of  rectangular  cross-section,  when  other  conditions  are  im- 
posed. 

If  we  had  supposed  the  sections  circular,  then  I  =  JTTT**, 
and  this  being  substituted  for  I  in  the  general  expression  foi 


144  CIVIL   ENGINEERING. 

the  stress  on  a  unit  of  surface  farthest  from  the  neutral  axis 
a  similar  process  would  enable  us  to  determine  the  form  of 
the  beam. 

Hence,  knowing  the  strains  to  which  any  piece  of  a  structure 
is  to  be  subjected,  we  may  determine  its  form  and  dimensions 
such  that  with  the  least  amount  of  material  it  will  successfully 
resist  these  strains. 


BELATTON    BETWEEN     STRESS    AND    DEFLECTION    PRODUCED    BY  A 
BENDING    FORCE. 

216.  Within  the  elastic  limit,  the  relation  between  the 
greatest  stress  in  the  fibres  and  the  maximum  deflection  of 
the  beam  produced  by  a  bending  force,  may  be  easily  deter- 
mined. 

Take  a  rectangular  beam,  supported  at  the  ends  and  loaded 
at  its  middle  point. 

The  third  of  equations  (89)  gives  for  this  case 


x 
and  solving  with  respect  to  W,  we  have 


in  which  W  is  the  load  on  the  middle  point  of  the  beam. 

The  maximum  deflection  produced  by  a  load,  2W,  in  this 
case  has  been  found,  the  length  of  beam  being  2£,  to  be 

W 

J-S*W 

Substituting  for  I,  W,  and  I,  the  proper  values,  we  have 

W     73 

* 


Solving  with  respect  to  W,  and  placing  it  equal  to  the  value 
of  W  obtained  from  eq.  (89),  we  have 


from  which  we  get 

R/=  >'; 


OBLIQUE  FORCES. 


145 


Hence,  knowing  the  deflection  and  the  coefficient  of  elas- 
ticity, the  greatest  stress  on  the  unit  can  be  obtained  and  the 
converse. 


FORCES  ACTING  OBLIQUELY. 

217.  The  forces  acting  on  the  beam  have  been  supposed  to 
be  in  the  plane  of,  and  perpendicular  to,  the  mean  fibre. 

The  formulas  deduced  for  this  supposition  are  equally 
applicable  if  the  forces  act  obliquely  to  the  mean  fibre. 

Suppose  a  force  acting  obliquely  in  the  plane  of  the  mean 
fibre,  it  can  be  resolved  into  two  components,  one,  P,  perpen- 
dicular, and  the  other,  Q,  parallel  to  the  fibre.  The  com- 
ponent P  will  produce  deflection,  and  the  component  Q, 
extension  or  compression  depending  on  the  angle,  whether 
obtuse  or  acute,  made  by  the  force  with  the  piece. 

The  strains  caused  by  each  of  the  components  can  be  deter- 
mined as  in  previous  cases. 

For  suppose  the  force  applied  in  the  plane  of  the  axis  of 
a  beam,  at  F  (Fig.  35),  and  let  x  be  the  distance  to  any 
tion,  as  K,  measured  on  the  axis  of  the  beam  E  F. 


FIG.  35. 


FIG.  36. 


Let 


Z  =  E  F,  the  length  of  the  beam,  and  a  =  the  angle  made 
by  the  axis  E  F  with  the  vertical. 
10 


146  CIVIL   ENGINEERING. 

The  bending  moment  at  any  section,  as  K,  is  equal  to 


sin 


and  its  value  for  the  dangerous  section  will  be  Wl  sin  or, 
I  being  the  greatest  lever  arm  of  W. 

The  greatest  stress  caused  by  P  on  the  unit,  at  the  danger- 
ous section  of  a  rectangular  beam,  b  and  d  being  the  dimen- 
sions of  cross-section,  will  be 

_  Wl  sin  a 

6— w 

The  stress  caused  by  Q  on  the  unit  will  be  either  com- 
pressive,  as  Fig.  (35),  or  tensile,  as  Fig.  (36),  and  its  intens- 
ity will  be 

W  cos  a 

bd     ' 

The  total  stress  on  the  unit  subjected  to  the  greatest  strain 
will  therefore  be 

"W7  sin  a        W  cos  a 

~W~  ~bd~' 

If  a  value,  as  R',  be  assumed  as  the  limit  of  the  stress  on 
the  unit  of  material,  it  will  be  necessary  to  deduct  from  B' 
the  intensity  of  the  stress  caused  by  Q,  so  as  to  avoid  de- 
veloping a  greater  stress  on  the  unit  than  that  assumed,  or, 
we  must  have  at  the  dangerous  section  for  a  rectangular 
beam, 


.     .   (97) 
and  in  general, 


STRENGTH    OF   BEAMS    TO    RESIST   TWISTING. 

218.  Strains  of  torsion  are  not  common  in  structures  and 
are  prevented  by  distributing  the  loads  symmetrically  over 
the  pieces,  making  the  resultants  of  the  straining  forces 
intersect  the  axes  of  the  pieces. 

Whenever  such  a  strain  does  exist,  the  intensity  of  the 
stress  may  be  determined  by  the  use  of  formula  (79).  In 
determining  the  value  of  Tt  by  this  formula,  the  experiment 
must,  as  in  the  case  of  transverse  strain,  be  made  upon  apiece 
similar  in  form  to  that  for  which  the  stress  is  to  be  found. 


ROLLING   LOADS.  147 

If  the  piece  be  circular  .in  cross  section,  formula  (79)  may 
be  placed  under  the  form, 


which  gives  the  force  necessary  to  produce  rupture  by  twist- 
ing. 

It  will  be  seen  that  the  modulus  of  torsion  is  independent 
of  the  length  of  the  piece,  being  dependent  upon  the  mo- 
ment of  the  twisting  couple  and  upon  the  form  and  dimen- 
sions of  the  cross-section. 

The  length  of  the  piece  affects  the  value  of  the  angle  of 
torsion,  a  ;  the  total  angle  being  greater  as  I  is  greater.  In 
using  formula  (77)  a  limit  should  be  assumed  for  a  such  that 
the  limit  of  torsional  elasticity  shall  not  be  passed. 

ROLLING  LOADS. 

219.  Systems  of  forces,  the  points  of  application  of  which, 
like  those  of  stationary  loads,  do  not  move,  have  been  the 
only  kinds  considered  in  the  previous  discussions. 

Many  structures,  such  as  bridges  for  example,  are  built  to 
sustain  loads  in  motion,  the  load  coming  upon  the  structure 
in  one  direction  and  moving  off  in  another.  A  load  of  this 
kind  is  called  a  moving,  a  rolling,  or  live  load,  to  dis- 
tinguish it  from  the  stationary  kind  usually  called  a  dead 
load. 

220.  In  determining  the  strength  of  a  beam  to  resist  the 
stresses  developed  by  a  live  load/it  is  necessary  to  determine 
the  positions  the  load  should  have  that  will  cause  the  greatest 
bending  moment  and  the  greatest  transverse  shearing  strain 
at  any  section  of  the  learn. 

Let  the  beam  (Fig.  37)  be  horizontal,  uniformly  loaded, 
and  strained  by  a  uniformly  distributed  live  load  that  grad- 
ually covers  the  entire  beam.  Let 

2Z  =  A  B,  the  length  of  the  beam  ; 

w  =  the  weight  of  the  uniform  stationary  load  on  the 
unit  of  length  ; 

w'  =  the  weight  of  the  rolling  load  per  unit; 

m  —  the  length  of  the  rolling  load  in  any  one  position  ; 

n  =  the  length  of  beam  not  covered  by  the  rolling  load  ; 

Bj,  KS,  the  reactions  at  the  points  of  support. 

Take  the  origin  of  co-ordinates  at  A,  the  axes  X  and  Y  as 
in  the  previous  cases,  and  suppose  the  live  load  to  have  come 
on  at  the  end  A,  and  to  occupy,  in  one  its  positions,  the 
space  from  A  to  D. 


148 


CIVIL   ENGINEERING. 


The  reactions  at  the  points  of  support,  due  to  the  uniform 
load  on  the  beam  and  the  live  load  from  A  to  D,  are 


EI  =  wl  +  w'm  — ^j— ,  and  E^  =  wl  +  w'm  jy . 

A  s 

x* 

I 

ii — *~  */ 


FIG.  37. 

The  bending  moment  at  any  section  whose  abscissa  is  #, 
and  which  lies  between  A  and  D,  for  this  position  of  the  load, 
is 

M  =  -  "Rjx  +  (w-+  w')-,     .    .    (99) 
and  for  any  section  between  D  and  B,  the  abscissa  being  a?, 

•m).     .     (100) 

*j  41 

and,  as  seen,  increases  as  m  increases.  The  bending  mo- 
ment will,  therefore,  be  greatest  when  m  is  greatest,  or  when 
m=  21.  Hence, 

M  r=  (w  -|-  W'}    (  — lx  J       .      .      (101) 

is  the  expression  for  the  greatest  bending  moment  at  any 
section  'of  the  beam,  and  it  exists  when  the  rolling  load  covers 
the  whole  beam. 

The  shearing  stress  at  any  section  between  A  and  D  is 

S'  =  (w  +  w')  x  -  K!     .     .     .     (102) 
and  for  any  section  between  D   and  B  is 

S'  =  (wx  +  w'm)  -  Ej     .     .     .  (103) 


ROLLING    LOADS.  149 

in  which  substituting  for  1^  its  value,  we  have 

S'  =  w  (x  -  1)  -  w'  (m  -  ^--#)    -    (104) 
and 

S'  =  w  (x  -  1)  +  w'  tg-  .    .     .    .     (105) 

from  which  the  shearing  stress  at  any  section  is  obtained. 

Let  x  be  the  abscissa  of  the  section,  D,  at  the  end  of  the  live 
load  in  any  one  of  its  positions  as  its  moves  from  A  toward 
B.  Substituting  x  for  x  in  eq.  (105)  we  have 

S"=w(x'-l)  +  w'^.    .     .    (106) 

4t 

for  the  shearing  stress  at  this  section  when  the  live  load 
extends  to  D. 

If  the  rolling  load  extends  entirely  over  the  beam,  the 
shearing  stress  at  any  section  is 

S'  =  (w  +  w')  (x  -  Z)  .     .    .     (107) 
and  for  the  section  D, 


which  may  be  written 

&"  =  w(x'  -l)+w'(x'-l).    .    (108) 

The  values  of  S"  at  the  section  0,  for  the  positions  of  these 
two  loads,  one  extending  to  D  and  the  other  entirely  over  the 
beam,  only  differ  from  each  other  in  the  terms,  w'  (x'  —  T) 

i     ,m2 
and  w  -JT  . 

4:1 

Since  2Z  =  m  +  n,  we  may  write 

w'  j       ^      w'     m* 

w>  (a/_  Q  ==  ^(m  -  n),  and   w  ^  ==  ?  ^—. 

Bv   comparing  —  —  —  with  m  —  n,  it  is  seen  that  the 
J  ft-ra  4-  n 

term  w'  (x'  —  T)  is  less  than  w'^-  whenever  m>l,or  at  any 

section  of  a  beam  the  greatest  shearing  stress  occurs  when 
the  moving  load  covers  the  longer  of  the  two  segments  into 
which  the  section  divides  the  beam. 


150  CIVIL  ENGINEERING. 

"When  the  rolling  load  covers  the  longer  segment,  the 
shearing  stress  is  said  to  be  a  main  shear ;  when  it  covers 
only  the  shorter  segment,  it  is  called  a  counter  shear. 

the  difference  in  the  intensity  of  the  shearing  stress,  at  a 
given  section,  caused  by  a  partial  rolling  ^  load  and  by 
one  that  covers  the  beam  can  be  shown  graphically. 

The  term,  w  (x  —  I),  in  equation  (105),  expresses  the  inten- 
sity of  the  shearing  stress  at  any  section  caused  by  the  dead 

load ;  the  term,  wr  —j  expresses  the  shearing  stress  at  the 
4^ 

sections  between  D  and  B  caused  by  the  live  load.  If  we  place 
y'  =  w  (x  —  I)  and  y'  =  —  m2,  two  equations  will  be  formed, 

^tv 

one  that  of  a  right  line,  the  other  a  parabola,  in  which  the 
ordinates  represent  the  shearing  stresses  caused  by  these 
loads.  Construct  the  parabola,  and  let  A  0  S'  be  the  arc 
determined.  The  ordinate  D  F  of  this  arc  will  represent  the 
shearing  stress  at  the  end  section  D,  and  at  all  sections 
between  D  and  B  produced  by  the  live  load,  A  D,  in  this 
position. 

When  the  live  load  covers  the  beam,  the  total  shearing 
stress  at  any  section  is  given  by  equation  (108).  That  part 
of  the  stress  produced  by  the  live  load  is  expressed  by  the 
term  w'  (x'  —  1),  which  is  the  ordinate  of  aright  line  passing 
through  C  and  S'.  No  ordinate  of  this  line  between  C  and  B 
is  equal  in  length  to  the  corresponding  ordinate  of  0  F  S'; 
hence,  the  shearing  stress  in  any  section  between  C  and  D 
is  greater  when  the  live  load  extends  from  A  to  the  section 
considered,  than  when  it  extends  entirely  over  the  beam. 

Let  m  and  x  have  simultaneous  and  equal  values  in 
equation  (105)  and  the  equation  will  be  that  of  a  parabola,  the 
ordinates  of  which  will  express  the  intensity  of  the  shearing 
stress  in  that  section  coinciding  with  the  end  of  the  moving 
load  in  all  of  its  positions. 

It  will  be  seen  that  this  parabola  intersects  the  axis  of  X 
between  A  and  C,  which  shows  that  there  is  a  section  of  the 
beam  at  which  there  is  no  shearing  stress  when  the  end  of  the 
rolling  load  reaches  it.  The  expression  for  the  distance  from 
the  origin  to  this  section  may  be  obtained  by  placing  the 
second  member  of  eq.  (105)  equal  to  zero,  and  solving  it  with 
respect  to  x  ;  there  results 

.  (109) 


An   equal   moving  load   coming  on    the  beam    from   B 
produces  a  similar  effect  to  that  of  the  one  coming  from  A, 


LIMITS   OF  PRACTICE.  151 

It  therefore  follows  that  there  is  a  point  of  "no  shear- 
ing "  beween  B  and  C,  and  that  this  point,  in  this  case,  coin- 
cides with  the  section  at  the  rear  end  of  the  rolling  load 
coming  from  A  as  it  rolls  off  the  beam.  These  points  of 
"  no  shear  "  are  of  interest  in  "  built "  beams  or  beams  com- 
posed of  several  pieces. 

LIMITS  OF  PRACTICE. 

221.  Until  quite  recently,  comparatively  speaking,  it  was 
the  custom  of  most  builders,  in  planning  and  erecting  a 
structure,  to  fix  the  dimensions  of  its  various  parts  from  pre- 
cedent, that  is,  by  copying  from  structures  already  built. 

So  long  as  the  structure  resembled  those  already  existing 
that  had  stood  the  test  of  time,  this  method  served  its  pur- 
pose. But  when  circumstances  forced  the  builder  to  erect 
structures  different  from  any  in  existence  or  previously  known, 
and  to  use  materials  in  a  way  in  which  they  had  never  before 
been  applied,  the  experience  of  the  past  could  no  longer  be 
his  guide.  Practical  sagacity,  a  most  excellent  and  useful 
qualification,  was  not  sufficient  for  the  emergency.  Hence 
arose  the  necessity  that  the  builder  should  acquire  a  thorough 
knowledge  of  the  theory  of  strains,  the  strength  of  materials, 
and  their  general  properties. 

The  principal  object  of  "strength  of  materials "  is  to  de 
termine  the  stresses  developed  in  the  different  parts  of  a  struc- 
ture, and  to  ascertain  if  the  stresses  are  within  the  adopted 
limits.  And  as  a  consequent,  knowing  the  strains,  to  deter- 
mine the  forms  and  dimensions  of  the  different  parts,  so  that 
with  the  least  amount  of  material  they  shall  successfully  re- 
sist these  strains. 

The  limits  adopted  vary  with  the  materials  and  the  charac- 
ter of  the  strain.  The  essential  point  is  that  the  limit  of 
elasticity  of  the  material  should  not  be  passed,  even  when  by 
some  unforeseen  accident  the  structure  is  subjected  to  an  un- 
nsual  stress.  The  adopted  limit  to  be  assigned  is  easily 
selected  if  the  limit  of  elasticity  be  known  ;  but  as  the  latter 
is  obtained  with  some  difficulty,  certain  limits  of  practice 
have  been  adopted. 

In  many  cases  this  practice  is  to  arbitrarily  assume  some 
given  weight  as  the  greatest  load  per  square  inch  on  a  given 
material,  and  to  use  this  weight  for  all  pieces  of  the  same 
material.  From  the  varying  qualities  of  the  same  material  it 
is  easily  seen  that  this  method  of  practice  differs  but  little 
from  a  "  mere  rule  of  thumb." 

The  most  usual  practice,  especially  for  structures  of  im- 
portance, as  bridges,  is  to  determine  the  breaking  weights  or 


152  CIVIL   ENGINEERING. 

ultimate  strength  of  the  different  parts,  and  take  a  frac- 
tional part  of  this  strength  as  the  limit  to  be  used.  The  re- 
ciprocal of  this  fraction  is  called  the  factor  of  safety. 

A  more  accurate  method  would  be  to  calculate  the  dimen- 
sions of  the  pieces  necessary  to  resist  the  strains  produced  by 
the  maximum  load,  and  then  enlarge  the  parts  sufficiently  to 
give  the  strength  determined  by  the  factor  of  safety. 

When  the  structure  is  one"  of  great  importance,  actua? 
experiments  should  be  made  on  each  kind  of  material  used  fa 
its  construction,  so  that  the  values  deduced  for  the  ultimate 
strength  shall  be  as  nearly  correct  as  possible. 

222.  These  factors  of  safety  are  arbitrarily  assumed,  being 
generally  about  as  follows : 

Material.  Factor  of  safety. 

Steel  and  wrought  iron 3 

Cast  iron 6 

Timber 6 

Stone  and  brick , 8  to  10. 

These  are  for  loads  carefully  put  on  the  structure. 

If  the  materials  and  workmanship  were  perfect,  these  factors 
could  be  materially  reduced. 

It  has  been  shown  (Art.  160)  that  the  work  expended  by 
the  sudden  application  of  a  given  force,  W,  is  equal  to  that 
expended  by  2W  if  applied  gradually  at  a  uniform  rate 
from  zero  to  2W.  Hence  a  force,  W,  applied  suddenly  to 
a  beam  will  produce  the  same  strain  on  the  beam  as  2W 
applied  gradually. 

A  rolling  load  moving  swiftly  on  a  structure  approximates 
nearly  to  the  case  of  a  force  suddenly  applied. 

Hence,  for  rolling  loads,  the  factors  of  safety  should  be 
doubled. 


CURVED  BEAMS. 

223.  A  beam  which  before  it  is  strained  has  a  curvilinear 
shape  in  the  direction  of  its  length  is  called  a  curved  beam. 
The  curve  given  to  the  mean  fibre  is  usually  that  of  a  cir- 
cular or  a  parabolic  arc. 

For  the  purposes  of  discussing  the  strains  on  beams  of  this 
class,  it  is  supposed  that: 

1.  The  beam  has  a  uniform  cross-section ; 

2.  That  its  cross-section  is  a  plane  iigure,  which  if  moved 
along  the  mean  fibre  of  the  beam  and  normal  to  it,  keeping 


CURVED   BEAMS.  153 

the  centre  of  gravity  of  the  plane  figure  on  the  mean  fibre, 
would  generate  the  solid  ;  and 

3.  That  the  dimensions  of  the  cross-section  in  the  direction 
of  the  radius  of  curvature  of  the  mean  fibre  are  very  small 
compared  with  the  length  of  this  radius. 

If  the  beam  be  intersected  by  consecutive  planes  of  cross- 
section,  the  hypotheses  adopted  for  a  straight  beam  subjected 
to  a  cross  strain  are  assumed  as  applicable  to  this  case. 

224.  General  equations. — Suppose  the  applied  forces  to 
act  in  the  plane  of  mean  fibre,  let  it  be  required  to  deter- 
mine the  relations  between  the  moment  of  resistance 
at  any  section  and  the  moment  of  the  external  forces 
acting  on  the  beam. 

Let  E  F  (Fig.  38)  be  a  curved  beam  ;  the  ends  E  and  F  so 
arranged  that  the  horizontal  distance  between  them  shall 
remain  constant. 


Km 

FIG.  3& 

.Let  A  B  be  any  cross-section.  The  external  forces  acting 
on  either  side  of  this  section  are  held  in  equilibrium  by  the 
resistances  developed  in  this  section.  Suppose  A  B  to  be  fixed, 
and  let  C'D'  be  the  position  assumed  by  the  consecutive 
section  under  the  action  of  the  external  forces,  on  the  right 
of  A  B.  The  resultant  of  these  external  forces  may  be  resolved 
into  two  components,  one  normal  and  the  other  parallel  to  the 
tangent,  to  the  curve  of  the  mean  fibre  at  0.  Represent  the 
former  by  F,  the  latter  by  F,  and  by  M,  the  sum  of  the 
moments  of  the  external  forces  around  the  neutral  axis  in  the 
section  A  B. 

The  fibre  ab  is  elongated  by  an  amount  be,  proportional  to 
its  distance  from  the  neutral  axis. 


154-  CIVIL  ENGINEERING. 

The  force  producing  this  elongation  is 
Eg  x  l>c 


or  since  ah  may  be  considered  equal  to  0  0', 

Ea  x  1)0 
OCX    ' 

in  which  E  is  the  co-efficient  of  elasticity  and  a  the  area  oi 
cross-section  of  the  fibre,  ah. 
Hence,  there  obtains  to  express  the  conditions  of  equilibrium, 


(110) 


.Represent  by  p  and  />',  the  radii  of  curvature,  R  0'  and  R'O'. 

The  triangle,  #R£,  has  its  three  sides  cut  by  the  right  line, 
R'C'.  Hence  the  product  of  the  segments,  R  0',  fo,  and  aR'  is 
equal  to  the  product  of  the  three  segments,  R  R',  50',  and  ac. 

Substituting  p  for  R  0',  p  —  p'  for  R'R,  and  p'  for  #R',  since 
Q'b  is  very  small  in  comparison  with  pf,  and  we  have 

p  x  Ic  x  p'  =  (p  —  p')  x  bO'  x  ac. 
From  which  we  get 


OG  pp  p  p 

Since  ac  differs  from  00'  by  an  infinitely  small  quantity, 

"bo 

the  expression  obtained  for  —  may  be  taken  as  the  value  of 
>    Substituting  this  value  for        ,,  in  the  second  of  equa- 


tions (110),  we  get. 

E  X        - 


This  sum,  S(a  x  JO72),  is  the  moment  of  inertia  of  the 
cross-section  taken  with  respect  to  the  neutral  axis  passing 
through  the  centre  of  gravity  of  the  section.  Kepresenting 
this  by  I,  equation  (111)  may  be  written 


M  r 

which  is  the  general  equation,  showing  the  relation  existing 


CURVED   BEAMS. 


155 


between  the  moments  of  resistances  of  any  section  and  the 
moments  of  the  external  forces  acting  on  that  section. 

225  Displacement  of  any  point  of  the  curve  of  mean 
fibre. — Let  A  B  (Fig.  39)  be  the  curve  of  mean  fibre  before 
the  external  forces  are  applied  to  the  beam. 


FIG.  39. 

Take  the  origin  of  co-ordinates  at  the  highest  point,  C,  and 
the  axes  X  and  Y  as  shown  in  the  figure. 

Let  D  be  any  point  whose  co-ordinates  are  x  and  y,  and 
represent  by  <f>  the  angle  made  by  the  plane  of  cross-section 
at  D  with  the  axis  of  Y. 

Suppose  the  external  forces  applied,  and  denote  by  xf  and 
y'  the  co-ordinates  of  D  in  its  new  position,  and  by  <f>'  the 
new  angle  made  by  the  plane  of  cross-section  with  the  axis  of 
Y. 

It  is  supposed  that  the  displacement  of  the  point,  D,  is  so 
slight  that  M  remains  unchanged. 

From  the  calculus  we  have 

--  —         A      '  —  — 

in  which  dz  and  dz'  are  the  lengths  of  the  elementary  prism 
before  and  after  the  strain  measured  along  the  mean  fibre. 
Since  they  differ  by  an  infinitely  small  quantity  from  each 
other,  by  making  dz  =  dz'  and  substituting  in  equation  (112) 
we  get 


El 
Integrating  we  obtain 


..   .   .   (H3) 


156  CIVIL  ENGINEEEING. 

The  component  force,  parallel  to  the  tangent  at  D,  acts  in 
the  direction  of  the  length  of  the  fibre.  Since  the  points  E 
and  F  are  fixed,  this  force  produces  a  strain  of  compression 
on  the  fibre.  The  length  of  this  fibre,  after  compression 
between  the  two  consecutive  planes,  is  represented  by  dfc', 
and  is 


The  values  of  cos  <£,  sin  <£,  cos  <£',  and  sin  <£'  may  be  written 
as  follows  : 

dx  dy 

cos0  =  ^        sin*  =  ^ 

da/  dy1 

' 


Substituting,  in  the  last  two  of  these,  the  value  just  found 
for  dz  ',  we  get 

da/  _  dy' 

cos  0  =       .         >b       and  sin  <£'  =  * 


If  $'  —  0  is  very  small,  we  may  write 

cos  <£'  =  cos  (f>  —  (<£'  —  <£)  sin  <^>,  and 
sin  <£'  =  sin  tj>  +  (</>'  —  ^>)  cos  <£. 

Substituting  these  values  of  cos  </>'  and  sin  $',  in  the  expres- 
eions  above,  and  solving  with  respect  to  dx'  and  dy  ',  we  get 

dx'  =  dz(l  -    -      (cos  <f>  -  (<£'  -  ^)  sin  <^>), 


(sin  <£  +  (f  -  0)  cos  0). 

Substituting  in  these  for  sin  <j>  and  cos  <£,  their  values  in 
terms  of  dz,  dy,  and  ^a?,  we  get 


CURVED   BEAMS.  157 

whence,  by  omitting  the  products  of  the  second  terms,  we  get 
dx'  —  dx  —  —  -pTT  dx  —  (<£'  —  $)  dy, 


y  +  (<f>f  —  <f>)  dx. 

•  r*  /  _  A_ 

Integrating,  there  obtains 

r  P  r 

-J  T^A dx~  I  W—  <W ^ 

y'  -  y  =  - 


(114) 


The  constants  of  integration  reduce  to  zero  for  both  equa- 
tions, since  from  hypothesis  there  is  no  displacement  of  the 
points  at  the  ends  of  the  curve  of  mean  fibre. 

If  the  beam  is  metal,  the  effect  of  temperature  must  be 
included  in  these  expressions  for  the  displacement. 

The  constant  of  integration  which  enters  the  expression  for 
<£'  —  <£,  also  enters  in  the  last  two  equations  for  the  displace- 
ment. The  value  of  this  constant  must  be  known  in  order  to 
determine  the  displacement.  Besides  the  constant,  there  is 
also  an  unknown  moment  in  M  which  must  be  determined. 

The  applied  forces  acting  on  the  beam  are  fully  given,  and 
are  taken,  as  before  stated,  in  the  plane  of  mean  fibre.  The 
reactions  at  the  points  of  support  are  not  known,  and  must  be 
determined. 

Let  Xx  represent  the  algebraic  sum  of  all  the  components 
of  the  applied  forces  parallel  to  the  axis  of  X ;  Yl  the  sum  of 
the  components  parallel  to  the  axis  of  Y ;  R!  and  R^  the 
vertical  components  of  the  reactions  at  A  and  B,  respectively ; 
and  Q!  and  Q2  the  horizontal  components  of  these  reactions. 

For  equilibrium,  there  obtains, 

Xt  +  Qi  -  Q2=  0,       l 


In  the  last  equation,  /^  represents  the  sum  of  the  momenta 
of  the  known  applied  forces  taken  with  respect  to  the  point 
of  support,  A,  h,  and  4>  tne  lever  arms  of  J^  and  Q2,  with 
respect  to  the  same  point. 

We  have  three  equations  and  four  unknown  quantities.  By 
introducing  the  condition  that  the  point  B,  shall  occupy  the 


158 


CIVIL    ENGINEERING. 


same  position  after  the  application  of  the  forces  as  it  had  be- 
fore, that  is,  befisced,  a  fourth  equation  may  be  obtained,  and 
the  problem  made  determinate. 

To  express  this  last  condition,  let  a^  and  yt  be  the  co-ordi- 
nates of  the  extremity  B  (Fig.  40),  x  and  y  the  co-ordinates 


FIG.  40. 

of  any  point  as  D,  and  $  the  angle  made  by  the  tangent  line  at 
D  with  the  axis  of  X.  Represent  by  TV  the  sum  of  the  com- 
ponents of  the  applied  forces  parallel  to  the  tangent  DT,  and 
by  fjL  the  sum  of  the  moments  of  the  applied  forces  with  re- 
spect to  to  the  section  at  D. 

The  bending  moment  at  D  will  be 

M  =  Ai  +  Qi(^-y)-Bi(<Bi-<B)    .    .    (116) 
and  for  the  force  acting  in  the  direction  of  the  tangent  DT, 
P  =  T!  +  Q8  cos  <£  +  R2  sin  <£.    .    .    .    (117) 

In  these  two  equations,  whenever  the  applied  forces  are  given, 
/tt,  Tb  y±  —  y,  and  a?i  —  a?,  are  known  functions  ;  but  R.J  and 
Q2  are  unknown  constants. 
But  from  the  third  of  equations  (115)  we  have 


which  substituted  in  the  expressions  just  obtained  for  M  and 
P  give  them  in  terms  of  one  unknown  constant  and  known 
functions. 
We  are  now  able  to  find  the  values  of  the  constant  of  in- 


CURVED   BEAMS.  159 

tegration  before  referred  to,  and  the  component  Q2.  Know- 
ing the  latter,  those  of  Q1?  1^,  and  R3  are  easily  found. 

226.  Having  found  all  the  external  forces  acting  on  the 
beam,  the  intensity  of  the  stress  on  any  cross-section  may  be 
determined. 

The  stress  on  the  unit  of  area  of  any  cross-section,  at 
the  distance  y  from  the  neutral  axis,  is 


in  which  P  and  F  are  the  components  of  the  external  forces, 
perpendicular  and  parallel  to  the  plane  of  cross-section  ;  A, 
the  area  of  the  cross-section  ;  I,  its  moment  of  inertia  ;  and 
M  the  bending  moment  of  the  external  forces  with  respect  to 
the  neutral  axis  of  the  cross-section. 

227.  In  chapters  IV.  and  Y.  of  his  "  Cours  de  Hecanique 
Appliquee,"  M.  Bresse  has  given  a  complete  discussion  of  the 
strains  in  curved  beams  resting  on  two  points  of  support,  pro- 
duced by  external  forces  acting  in  the  plane  of  mean  fibre  ; 
the  cross-section  of  the  beam  being  uniform  and  the  curve  of 
mean  fibre  a  circular  arc. 

He  has  deduced  exact  formulas  for  the  horizontal  thrust  ^ 
Q2,  and  reduced  these  formulas  to  forms  of  easy  application 
for  the  cases  most  commonly  used.  He  has  besides  con- 
structed tables  containing  the  values  of  the  quantities  found 
in  the  formulas,  under  the  different  suppositions  usually 
made. 

If  the  beam  has  its  ends  in  the  same  horizontal  plane  and 
is  loaded  symmetrically  with  reference  to  its  middle  point,  or 
strained  by  vertical  loads  only,  Q!  and  Q2  are  equal. 

The  following  formula  for  a  load  uniformly  distributed 
over  the  beam,  along  the  mean  fibre,  when  the  rise,  H  C,  is 
small  compared  with  the  span,  A  B,  is  given  by  him  : 


in  which  w  is  the  load  on  the  unit  of  length  of  the  curve ;  p, 
the  radius  of  the  curve  of  mean  fibre ;  <£,  the  half  of  the 
angle,  A  0  B,  included  between  the  radii  drawn  to  the  ex- 
tremities A  and  B  ;  2Z,  the  length  of  the  chord,  A  B ;  /,  the 
rise,  H  C  ;  and  &,  the  radius  of  gyration  of  the  cross-section  of 
the  beam. 


160 


CIVIL  ENGINEERING. 


And  under  the  same  circumstances,  the  load  being  dis- 
tributed on  the  beam  uniformly  over  the  chord  A  B  or  a 
horizontal  tangent  at  C,  he  gives  the  following  formula : 


(119) 


228.  Suppose  a  curved  beam,  the  mean  fibre  being  a  pa- 
rabolic arc,  to  be  strained  by  a  uniform  load  distributed  so 
as  to  be  directly  proportional  to  its  horizontal  length.  An 
approximate  method  of  determining  the  stresses  is  as 
follows : 

Let  A  V  (Fig.  41)  be  half  of  the  curve  of  mean  fibre ;  V,  the 
origin  of  coordinates;  the  tangent  V  X  to  be  the  axis  of  X,  and  V  Y 


FIG.  41. 

the  axis  of  Y.  Let  D  and  D'  be  any  two  consecutive  points 
whose  abscissas  are  x  and  xf.  Denote  by  I  the  half -span  A  Y, 
by/  the  rise  V  Y,  and  by  w  the  weight  on  the  unit  of  length 
measured  on  V  X. 

Assuming  the  bending  moment  at  V  to  be  zero,  suppose  the 
right  half  of  the  beam  to  be  removed.  The  equilibrium 
among  the  external  forces  acting  on  the  remaining  half  may 
be  preserved  by  the  substitution  of  a  horizontal  force,  H,  act- 
ing at  V.  The  external  forces  acting  on  the  beam  between  V 
and  any  section  as  D,  will  therefore  be  the  force  II,  the  weight 
wx,  and  the  reaction  at  D,  which  denote  by  P. 

Since  there  is  an  equilibrium  in  the  system  of  forces  acting 
on  the  arc  D  V,  the  intensities  of  these  forces  H,  P,  and  wx 
must  be  proportional  to  the  sides  of  the  triangle  DxT.  Since 
D  H  and  D'H  are  respectively  parallel  to  T#  and  D^  we  have 


CURVED   BEAMS.  1C1 

To?:  Da;::HD  :  D'H, 
or  H  :  wx  :  :  dx  :  dy, 

whence  dy  =      xdx. 


Integrating,  we  obtain 


Taking  this  between  the  limits  x  =  0  and  x  =  I,  there 
•nits 

w 


whence  H  =  |^    .......  (121) 

This  is  the  same  as  the  coefficient  outside  of  the  parenthesis 
in  the  expression  for  Q2  in  eq.  (119). 


But  P  = 

and  substituting  in  which  the  value  just  found  for  H,  we  get 


=W~  +  a?.    .    .    .    (122) 
y  be  deduced  dir 
H  x  AX=^VXxiVX, 


The  value  for  H  may  be  deduced  directly  by  moments. 
For  we  have 


whence  H  =  -^  . 

J/ 

These  expressions  show  that  P  is  least  at  V  and  greatest  at 
A,  and  that  H  is  the  same  throughout.     The  value  for  H  is 
independent  of  the  form  of  the  curve  of  mean  fibre,  whether 
parabolic,  circular,  or  other  shape. 
11 


162  CIVIL  ENGINEERING. 

Curved  beams  are  frequently  constructed  so  that  the  curve 
assumed  by  the  mean  fibre  under  the  action  of  the  load  is  that 
of  a  parabolic  arc,  the  vertex  being  at  the  highest  point. 

In  this  case,  the  direction  of  P  coincides  with  that  of  the 
tangent  to  the  curve  of  mean  fibre ;  the  bending  moment  at 
each  cross  section  is  zei  o ;  and  the  strain  is  one  of  compres- 
sion produced  by  P. 

If  the  two  halves  abut  against  each  other  at  V,  or  are  hinge- 
jointed  at  this  point,  the  assumption  that  the  bending  moment 
at  this  section  is  zero,  is  a  correct  one. 


CURVED   BEAMS   WITH   THE   ENDS   FIEMLY   FIXED. 

229.  The  curved  beam  in  the  foregoing  discussion  has  had 
the  analogous  position  of  a  straight  beam  resting  on  two  sup- 
ports. In  each  of  these  cases  the  beam  has  been  regarded  as 
continuous  between  the  points  of  support,  and  the  horizontal 
distance  between  these  points  as  constant. 

If,  in  addition,  the  condition  be  imposed  that  the  cross- 
sections  at  the  points  of  support  be  fixed  so  that  they  shall 
not  move  under  the  action  of  the  external  forces,  the  case 
becomes  analogous  to  that  of  a  straight  beam  whose  ends  are 
firmly  imbedded  in  a  wall.  And  there  will  be,  as  in  that  case, 
an  unknown  moment  at  the  points  of  support,  whose  value 
must  be  found  before  the  strains  on  the  beams  can  be  deter- 
mined. Having  found  this,  the  processes  of  obtaining  the 
strains  and  calculating  the  dimensions  of  the  beam  are  ana- 
logous to  those  already  used. 


PART   III 

FRAMING. 


CHAPTER  VIIL 

230.  The  art  of  construction  consists  mainly  in  giving  to  a 
structure  the  proper  degree  of  strength  with  the  least  amount 
of  material  necessary  for  the  purpose.     If  any  piece  be  made 
stronger  than  is  necessary,  the  superfluous  weight  of  this  piece 
will  in  general  be  transmitted  to  some  other  part,  and  the 
latter,  in  consequence,  will  be  required  to  sustain  a  greater 
load  than  it  should.     Hence,  the  distribution  and  sizes  of  the 
different  parts  of  a  structure  should  be  determined  before 
combining  the  parts  together. 

A  frame  is  an  arrangement  of  beams,  bars,  rods,  etc., 
made  for  sustaining  strains.  The  art  of  arranging  and  fit- 
ting the  different  pieces  is  called  framing,  and  forms  one  of 
the  subdivisions  of  the  art  of  construction.  It  follows,  then, 
from  the  previous  remark,  that  the  object  to  be  attained  in 
framing  is  to  arrange  the  pieces,  with  due  regard  to  lightness 
and  economy  of  material,  so  that  they  shall  best  resist,  with- 
out change  of  form  in  the  frame,  the  strains  to  which  the 
latter  may  be  subjected. 

231.  The  principal  frames  employed  by  engineers  are  those 
used   in  bridges,  centres   for  arches,  coffer-dams,   caissons, 
floors,  partitions,  roofs,  and  staircases. 

The  materials  used  in  their  construction  are  generally  tim- 
ber and  iron.  The  latter,  in  addition  to  superior  strength, 
possesses  an  advantage  over  wood  in  being  susceptible  of  re- 
ceiving the  most  suitable  form  to  resist  the  strains  to  which  it 
may  be  subjected. 

When  the  principal  pieces  of  a  frame  are  of  timber,  the 
construction  belong  to  that  branch  of  framing  known  aa 
carpentry. 

~~~ie  combination  of  the  pieces,  and  the  shape  of  a  frame 


164:  CIVIL  ENGINEERING. 

will  depend  upon  the  purposes  for  which  the  frame  is  to  be 
adapted  and  upon  the  directions  of  the  straining  forces. 

One  of  the  main  objects  in  the  arrangement  of  a  frame  is 
to  give  the  latter  such  a  shape  that  it  will  not  admit  of  change 
in  its  figure  when  strained  by  the  forces  which  it  is  intended 
to  resist.  This  is  usually  effected  by  combining  its  parts  so 
as  to  form  a  series  of "  triangular  figures,  each  side  of  the 
latter  being  a  single  beam.  If  the  frame  has  a  quadrilateral 
shape,  secondary  pieces  are  introduced  either  having  the 
positions  of  the  diagonals  of  the  quadrilateral,  or  forming 
angles  with  the  upper  and  lower  sides  of  the  frame.  These 
secondary  pieces  are  called  braces.  When  they  sustain  a 
strain  of  compression  they  are  termed  struts ;  of  extension, 
ties. 

The  strength,  and  hence  the  dimensions,  of  the  pieces  will 
be  regulated  by  the  strains  upon  the  frame.  Knowing  the 
strains  and  the  form  of  the  frame,  the  amount  of  stress  on 
each  piece  can  be  deduced,  and  from  this  the  proper  form 
and  particular  dimensions  of  each  piece. 

The  arrangement  of  the  frame  should  be  such  that,  after 
being  put  together,  any  one  piece  can  be  displaced  without 
disconnecting  the  others. 

When  practicable,  the  axes  of  the  pieces  should  be  kept  in 
the  plane  of  the  forces  which  act  to  strain  the  frame,  and  the 
secondary  pieces  of  the  frame  should  be  arranged  to  transmit 
the  strains  in  the  direction  of  their  lengths.  The  pieces  are 
then  in  the  best  position  to  resist  the  strains  they  have  to 
support,  and  all  unnecessary  cross-strains  are  avoided. 

The  essential  qualities  of  a  frame  are,  therefore,  strength, 
stiffness,  lightness,  and  economy  of  material. 


JOINTS. 

232.  The  joints  are  the  surfaces  at  which  the  pieces  of  a 
frame  touch  each  other ;  they  are  of  various  kinds,  according 
to  the  relative  positions  of  the  pieces  and  to  the  forces  which 
the  pieces  exert  on  each  other. 

Joints  should  be  made  so  as  to  give  the  largest  bearing  sur- 
faces consistent  with  the  best  form  for  resisting  the  particular 
strains  which  they  have  to  support,  and  particular  attention 
should  be  paid  to  the  effects  of  contraction  and  expansion  in 
the  material  of  which  they  are  made. 

In  planning  them  the  purpose  they  are  to  serve  must  be 
kept  in  mind,  for  the  joint  most  suitable  in  one  case  would 
oftentimes  be  tho  least  suitable  in  another. 


PLAIN   JOINTS.  165 


JOINTS    IN   TIMBER   WORK. 

233.  In  frames  made  of  timber,  the  pieces  may  be  joined 
together  in  three  ways;  by  connecting  them, 

"i.  End  to  end  ; 

2.  The  end  of  one  piece  resting  upon  or  notched  into  the 
face  of  another ;  and 

3.  The  faces  resting  on  or  notched  into  each  other. 

I.  Joints  used  to  unite  beams  end  to  end,  the  axes 
of  the  beams  being  in  the  same  straight  line. 

The  joint  used  to  lengthen  a  beam  is  either  a  plain  or  a 
scarfed  joint.  There  are  two  cases:  one  in  which  the 
beam  is  subjected  to  compressive  or  tensile  strains,  and  the 
other  in  which  it  is  subjected  to  a  cross  strain. 

234.  First.  Suppose  the  pieces  are  required  to  resist  strains 
in  the  direction  of  their  length. 


Plain  or  Butt  Joints. 

A  plain  joint  is  one  in  which  the  two  pieces  abut  end  to 
end,  as  shown  at  cd  (Fig.  42),  the  surface  of  the  joint  being 
perpendicular  to  the  axis  of  the  beam.  The  ends  of  the 
pieces  being  brought  together  are  fastened  to  prevent  dis- 
placement by  any  lateral  movement.  This  fastening  is 
usually  effected  by  bolting  to  the  beam,  on  each  side  of  the 
joint,  pieces  of  wood  or  iron.  A  joint  fastened  in  this  way 


:                 ( 

ii            1 

i     A 

::            1! 

! 

jl      » 
!!     **      ii 

1            •:            !! 

fl 

'           ;;            ii 

::            1 

FIG.  43— Represents  the  manner  in  which  two  beams  a  and  Z>  are  fished  by 
side  pieces  c  and  d  bolted  to  them. 

is  said  to  be  fished,  and  is  sometimes  called  a  fish  joint. 

A  plain  joint  is  a  good  one  when  the  onfy  strain  is  that  of 
compression.  It  is  recommended,  in  this  case,  to  place  h'sh- 
pieces  on  all  four  of  the  sides  of  the  beam,  to  prevent  any 
lateral  displacement  of  the  ends  that  might  be  caused  by 
shocks. 

If  the  strain  be  one  of  tension,  it  is  evident  that  the  strength 


166 


CIVIL   ENGINEERING. 


is  joint  (Fig.  42)  depends  entirely  upon  the  strength  of 
olts,  assisted  by  the  friction  of  the  fish-pieces  against 
Such  a  joint  would  seldom  be  used 


of  this 

the  bolts, 

the  sides  of  the  timber. 

for  tension. 

A  better  fastening  for  the  joint  would  be  that  in  which 
the  fish-pieces  were  let  into  the  upper  side  of  the  beam,  as 


3> 


FIG.  43 — Represents  a  joint  to  resist  extension,  iron  rods  or  bars  being  used 
to  connect  the  beams  instead  of  wooden  fish-pieces. 

shown  in  Fig.  44. 

Sometimes  the  beam   and   the  fish-pieces  have  shallow 
notches  made  in  them,  into  which  keys  or  folding  wedges  of 


FIG.  44— Represents  a  fished  joint  in  which  the  side  pieces  c  and  d  are  either 
let  into  the  beams  or  secured  by  keys  e,  e. 

hard  wood  as  e,  e  (Fig.  44)  are  inserted. 
Scarf  Joints. 

When  the  ends  of  the  pieces  overlap,  the  joint  is  called  a 
scarf  joint.  The  ends  of  the  pieces  are  fastened  together 
by  bolts,  to  keep  them  in  place.  An  example  of  a  simple 
scarf  joint  is  shown  in  Fig.  45,  that  is  sometimes  used  when 
the  beam  is  to  be  subjected  only  to  a  slight  strain  of  exten- 


FJG.  45. 


<jion.  A  key  or  folding  wedge  is  frequently  added,  notched 
equally  in  both  beams  at  the  middle  of  the  joint ;  it  serves 
to  bring  the  surfaces  of  the  joint  tightly  together. 


SCARF  JOINTS. 


167 


A  better  scarf  joint  is  made  by  cutting  the  ends  in  such  a 
manner  as  to  form  projections  on  one  which  fit  into  corre- 
sponding indentations  in  the  other,  as  shown  in  Fig.  46 


FIG.  46. 

The  total  lap  shown  in  this  figure  is  ten  times  the  thick- 
ness of  the  timber,  and  the  depth  of  the  notches  at  A  and  B 
are  each  equal  to  one-fourth  that  of  the  beam.  The  bolts  are 
placed  at  right  angles  to  the  principal  lines  of  the  joint. 

This  is  a  good  joint  to  resist  a  strain  of  tension,  since  the 
notches  at  A  and  B  allow  one-half  of  the  cross-section  of  the 
beam  to  be  utilized  in  resisting  the  tensile  strain. 

Another  form  of  scarf  joint  is  shown  in  Fig.  47.  A  joint 
made  in  this  shape  is  serviceable  to  resist  either  a  coinpres- 
sive,  or  a  tensile  strain  on  the  beam. 


d   \ 


I 


FIG.  47— Represents  a  scarf-joint  secured  by  iron  fish-plates  c,  c,  keys 
d,  d,  and  bolts. 

235.  Second.  Suppose  the  pieces  are  required  to  resist  a 
£ross  strain. 

In  this  case  the  scarf  joint  is  the  one  generally  used.  The 
joint  may  be  formed  by  simply  halving  the  beams  near  their 
ends,  as  shown  in  Fig.  47,  and  fastening  the  ends  of  the 
beams  by  fish-pieces  bolted  upon  the.  upper  and  lower  sides 
of  the  ends.  Keys  of  hard  wood  are  used  to  resist  the  longi- 
tudinal shear  along  the  lap  of  the  joint. 

A  more  usual  and  the  better  form  of  joint  for  this  case  is 
shown  in  Fig.  48. 


.  48— Represents  a  scarf-joint  for  a  cross-strain,  fished  at  bottom  by 
a  piece  of  wood  c. 


168  CIVIL  ENGINEERING. 

In  the  upper  portion  of  this  joint  the  abutting  surfaces  are 
perpendicular  to  the  length  of  the  beam  and  extend  to  a  depth 
of  at  least  one-third  and  not  exceeding  one-half  that  of  the 
beam.  In  the  bottom  portion  they  extend  one-third  of  the 
depth  and  are  perpendicular  to  the  oblique  portio'n  joining 
the  upper  and  lower  ones. 

The  lower  side  of  the  beam  is  fished  by  a  piece  of  wood  or 
iron  plate,  secured  by  bolts  or  iron  hoops,  so  as  to  better  resist 
the  tensile  strain  to  which  this  portion  of  the  beam  is  sub- 
jected. 

Third.  Suppose  the  beam  required  to  resist  a  cross-strain 
combined  with  a  tensile  strain. 

The  joint,  frequently  used  in  this  case,  is  shown  in  Fig.  49. 


a 


FIG.  49 — Represents  a  scarf -joint  arranged  to  resist  a  cross-strain  and  one 
of  extension.  The  bottom  of  the  joint  is  fished  by  an  iron  plate  ;  and  a 
folding  wedge  inserted  at  c  serves  to  bring  all  the  surfaces  of  the  joint 
to  their  bearings. 

II.  Joints  of  beams,  the  axes  of  the  beams  making  an 
angle  with  each  other. 

236.  In  the  previous  cases  the  axes  were  regarded  as  being 
in  the  same  straight  line.  If  it  be  required  to  unite  the  ends 
and  have  the  axes  make  an  angle  with  each  other,  this  may  be 
done  by  halving  the  beams  at  the  ends,  or  by  cutting  a  mortise 
in  the  centre  of  one,  shaping  the  end  of  the  other  to  fit,  and 
fastening  the  ends  together  by  pins,  bolts,  straps,  or  other 
devices.  The  joints  used  in  the  latter  case  are  termed 
mortise  and  tenon  joints.  Their  form  will  depend  upon 
the  angle  between  the  axes  of  the  beams. 


Mortise  and  Tenon  Joints. 

237.  When  the  axes  are  perpendicular  to  each  other,  the 
mortise  is  cut  in  the  face  of  one  of  the  beams,  and  the  end 
of  the  other  beam  is  shaped  into  a  tenon  to  fit  the  mortise,  as 
shown  in  Fig.  50. 

When  the  axes  are  oblique  to  each  other,  one  of  the  most 
common  joints  consists  of  a  triangular  notch  cut  in  the  face 
of  one  of  the  beams,  with  a  shallow  mortise  cut  in  the  bottom 


MORTISE   AND   TENON   JOINTS. 


159 


of  the  notch,  the  end  of  the  other  beam  being  cut  to  fit  the 
notch  and  mortise,  as  shown  in  Fig.  51. 


B 


FIG.  50 — Represents  a  mortise  and  tenon  joint  when  the  axes 

of  the  beams  are  perpendicular  to  each  other, 
o,  tenon  on  the  beam  A. 
ft,  mortise  in  the  beam  B. 
c,  pin  to  hold  the  parts  together. 

In  a  joint  like  this  the  distance  db  should  not  be  less  than 
one-half  the  depth  of  the  beam  A  ;  the  sides  ab  and  be  should 
l>e  perpendicular  to  each  other  when  practicable ;  and  the 


FlG.  51— Represents  a  mortise  and  tenon  joint  when  the 
axes  of  the  beams  are  oblique  to  each  other. 

thickness  of  the  tenon  d  should  be  about  one-fifth  of  that  of 
the  beam  A.  The  joint  should  be  left  a  little  open  at  c  to 
allow  for  settling  of  the  frame.  The  distance  from  J  to  the 
end  D  of  the  beam  should  be  sufficiently  great  to  resist  safely 
the  longitudinal  shearing  strain  caused  by  the  thrust  of  the 
team  A  against  the  surface  ab. 
Denote  by 

H  the  component  of  the  thrust,  parallel  to  the  axifl  of 
the  beam  B  D  ; 

I  the  breadth  in  inches  of  the  beam  B  D ; 


170  CIVIL   ENGINEERING. 

I  the  distance  in  inches  from  I  to  the  end  of  the 

beam  at  D  ;  and 
S  the  resistance  per  square  inch  in  the  beam  B  to  lon- 

gitudinal shearing. 
The  total  resistance  to  shearing  will  be  S  x  U,  hence 

S  x  U  =  H,  from  which  we  have 


The  value  of  S  for  the  given  material,  Art.  166,  being  sub- 
stituted in  this  expression,  will  give  the  value  for  I,  when  the 
Btrain  just  overcomes  the  resistance  of  the  fibres.  In  this 
case  the  factor  of  safety  is  ordinarily  assumed  to  be  at  least 
four.  Therefore  the  value  of  I,  when  the  adhesion  of  the 
fibres  is  depended  upon  to  resist  this  strain,  will  be 


S  being  taken  from  the  tables. 

A  bolt,  ef,  or  strap,  is  generally  used  to  fasten  the  ends 
more  securely. 

In  both  of  these  cases  the  beam  A  is  subjected  to  a  strain 
of  compression,  and  is  supported  by  B.  If  we  suppose  the 
beams  reversed,  A  to  support  B,  the  general  principles  for 
forming  the  joints  would  remain  the  same. 

Suppose  the  axes  of  the  beams  to  be  horizontal,  and  the 
beam  A  to  be  subjected  to  a  cross-strain,  the  circumstances 
being  such  that  the  end  of  the  beam  A  is  to  be  connected  with 
the  face  of  the  other  beam  B. 

In  this  case  a  mortise  and  tenon  joint  is  used,  but  modified 
in  form  from  those  just  shown. 

To  weaken  the  main  or  supporting  beam  as  little  as  possi- 
ble, the  mortise  should  be  cut  near  the  middle  of  its  depth ; 
that  is,  the  centre  of  the  mortise  should  be  at  or  near  the  neu- 
tral axis.  In  order  that  the  tenon  should  have  the  greatest 
strength,  it  should  be  at  or  near  the  under  side  of  the  joint. 

Since  both  of  these  conditions  cannot  be  combined  in 
the  same  joint,  a  modification  of  both  is  used,  as  shown  in 
Fig.  52. 

The  tenon  has  a  depth  of  one-sixth  that  of  the  cross-beam 
A,  and  a  length  of  twice  this,  or  of  one-third  the  depth  of  the 
beam.  The  lower  side  of  the  cross-beam  is  made  into  a  shoul- 
der, which  is  let  into  the  main  beam,  one  half  the  length  of 
the  tenon. 

Double  tenons  have  been  considerably  used  in  carpentry 


FASTENINGS.  371 

As  a  rule  they  should  never  be  used,  as  both  are  seldora  in 
bearing  at  the  same  time. 


FIG.  52.— A,  the  cross-beam. 

B,  cross-section  of  main  beam, 
i,  the  tenon. 

III.  Joints  used  to  connect  beams,  the  faces  resting  on 
or  notched  into  each  other. 

238.  The  simplest  and  strongest  joint  in  this  case  is  made 
by  cutting  a  notch  in  one  or  both  beams  and  fastening  the 
fitted  beams  together. 

If  the  beams  do  not  cross,  but  have  the  end  of  one  to  rest 
upon  the  other,  a  dove-tail  joint  is  sometimes  used.  In  this 
joint,  a  notch  trapezoidal  in  form,  is  cut  in  the  supporting 
beam,  and  the  end  of  the  other  beam  is  fitted  into  this  notch. 

On  account  of  the  shrinkage  of  timber,  the  dove-tail  joint 
should  never  be  used  except  in  cases  where  the  shrinkage  in 
the  different  parts  counteract  each  other. 

It  is  ajoint  much  used  in  joiner's  work. 

239.  The  joints  used  in  timber-work  are  generally  composed 
of  plane    surfaces.     Curved  ones  have  been   recommended 
for  struts,  but  the  experiments. of  Hodgkinson  would  hardly 
justify  their  use.     The  simplest  forms  are  as  a  rule  the  best, 
as  they  afford  the  easiest  means  of  fitting  the  parts  together. 


FASTENINGS. 

The  fastenings  used  to  hold  the  pieces  of  a  frame  together 
at  the  joints  may  be  classed  as  follows : 

1.  Pins,  including  nails,  spikes,  screws,  bolts,  and  wedges; 

2.  Straps  and  tiebars,  including  stirrups,  suspending-rods, 
etc. ;  and 

3.  Sockets. 

These  are  so  well  known  that  a  description  of  them  is  un- 
necessary. 


172  CIVIL  ENGINEERING. 


General  Rules  to  be  observed  in  the  Construction  of  Joints. 

241.  The  following  general  rules  should  be  observed  in  the 
construction  pf  joints  and  fastenings  for  frames  of  timber : 

I.  To  arrange  the  joints  and  fastenings  so  as  to  weaken  as 
little  as  possible  the  pieces  which  are  to  be  connected. 

II.  In  a  joint  subjected  to  compression,  to  place  the  abut- 
ting surfaces  as  nearly  as  possible  perpendicular  to  the  direc- 
tion of  the  strain. 

III.  To  give  to  such  joints  as  great  a  surface  as  practicable. 

IV.  To  proportion  the  fastenings  so  that  they  will  be  equal 
in  strength  to  the  pieces  they  connect. 

Y.  To  place  the  fastenings  so  that  there  shall  be  no  danger 
of  the  joint  giving  way  by  the  fastenings  shearing  or  crushing 
the  timber. 


JOINTS  FOR  IRON-WORK. 

242.  The  pieces  of  an  iron  frame  are  ordinarily  joined  by 
means  of  rivets,  pins,  or  nuts  and  screws. 


Riveted  Joints. 

243.  A  rivet  is  a  short,  headed  bolt  or  pin,  of  iron  or  other 
malleable  material,  made  so  that  it  can  be  inserted  into  holes 
in  the  pieces  to  be  fastened  together,  and  that  the  point  of 
the  bolt  can  be  spread  out  or  beaten  down  closely  upon  the 
piece  by  pressure  or  hammering.  This  operation  is  termed 
riveting,  and  is  performed  by  hand  or  by  machinery.  By 
hand,  it  is  done  with  a  hammer  by  a  succession  of  blows. 
By  machinery,  as  ordinarily  used,  the  heated  bolt  is  both 
pressed  into  the  hole  and  riveted  by  a  single  stroke.  If  a  ma- 
chine uses  a  succession  of  blows,  the  operation  is  then  known 
as  snap-riveting.  By  many  it  is  claimed  that  machine 
riveting  possesses  great  superiority  over  that  by  hand,  for 
the  reason  that  the  rivets  more  completely  fill  the  holes,  and 
in  this  way  become  an  integral  part  of  the  structure.  It  is 
doubtful  if  it  possesses  the  advantage  of  superior  strength  to 
any  marked  degree.  It  does  certainly  possess,  however,  the 
advantage  of  being  more  quickly  executed  without  damage 
to  the  heads  of  the  rivets. 

The  holes  are  generally  made  by  punching,  are  about  one- 
twentieth  of  an  inch  larger  than  the  diameter  of  the  rivet,  and 


NUMBER   OF    RIVETS.  173 

are  slightly  conical.  The  diameter  of  the  rivet  is  generally 
greater  than  the  thickness  of  the  plate  through  which  the  hole 
is  to  be  punched,  because  of  the  difficulty  of  punching  holes 
of  a  smaller  size.  Punching  injures  the  piece  when  the  latter 
is  of  a  hard  variety  of  iron,  and  for  this  reason  engineers  often 
require  that  the  holes  be  drilled.  Drilling  seems  to  be  the 
better  method,  especially  when  several  thicknesses  of  plates 
are  to  be  connected,  as  it  insures  the  precise  matching  of  the 
rivet  holes.  The  appearance  of  the  iron  around  a  hole  made  by 
punching  gives  a  very  fair  test  of  the  quality  of  the  iron. 

When  two  or  more  plates  are  to  be  riveted,  they  are  placed 
together  in  the  proper  position,  with  the  rivet-holes  exactly 
over  one  another,  and  screwed  together  by  temporary  screw- 
bolts  inserted  through  some  of  the  holes.  The  rivets,  heated 
red-hot,  are  then  inserted  into  the  holes  up  to  the  head,  and 
by  pressure  or  hammering,  the  small  end  is  beaten  down  fast 
to  the  plate.  In  a  good  joint,  especially  when  newly  riveted, 
the  friction  of  the  pieces  is  very  great,  being  sufficient  to  sus- 
tain the  working-load  without  calling  into  play  the  shearing 
resistance  of  the  rivets.  In  calculating  the  strength  of  the 
frame,  this  amount  of  strength  due  to  friction  is  not  consid- 
ered, as  it  cannot  be  relied  on  after  a  short  time  in  those  cases 
where  the  frame  is  subjected  to  shocks,  vibrations,  or  great 
changes  of  temperature. 


Number  and  Arrangement  of  Rivets. 

244.  The  general  rule  determining  the  number  is  that  the 
sum  of  the  areas  of  the  cross-sections  of  the  rivets  shall  be 
equal  to  the  effective  sectional  area  of  the  plate  after  the  holes 
have  leen  punched.  This  rule  is  based  on  the  theory  that  the 
resistance  to  shearing  strain  in  the  rivet  is  equal  to  the  tena- 
city of  the  plate. 

To  determine  the  proper  distance  bet-ween  the  rivets 
in  the  direction  of  any  row,  so  that  the  strength  of  the  rivets 
in  any  single  row  shall  be  equal  to  the  strength  of  the  section 
of  the  plate  along  this  row  after  the  holes  have  been  punched, 
let 

dy  be  the  diameter  of  the  rivet ; 

c,  the  distance  between  the  centres  of  consecutive  rivets ; 

a,  the  area  of  cross-section  of  the  rivet ; 

A',  the  effective  area,  between  two  consecutive  rivets,  of  the 
cross-section  of  the  plate  along  the  row  of  rivets ;  and 

t,  the  thickness  of  the  iron  plate. 


174  CIVIL  ENGINEERING. 

It  has  been  assumed  that 

T  =  S, 
and  the  rule  requires  that 

TA'  =  S  x  a,   or   -g-  =  -£,  -  1. 
We  have 

whence 

c  =  ^+d, (123) 

for  the  distance  from  centre  to  centre  of  tlie  consecutive 
rivets  in  any  one  row. 

English  engineers,  in  practice,  use  rivets  whose  diameters 
are  f,  f,  -J,  1,  1J,  and  1J-  inches,  for  iron  plates  J,  ^,  £,  £,  |, 
and  f  inches  thick,  respectively,  and  take  the  distance  from- 
centre  to  centre  at  2  diameters  for  a  strain  of  compression, 
and  2J  diameters  for  extension.  The  distance  of  the  centre 
of  the  extreme  rivet  from  the  edge  of  the  plate  is  taken  be- 
tween 1£  and  2  diameters. 

Instead  of  assuming  the  resistance  to  shearing  in  the  rivet 
equal  to  the  tenacity  of  the  iron  plate,  a  better  rule  would  be 
to  make  the  product  arising  from  multiplying  the  sum  of  the 
areas  of  the  cross -section's  of  the  rivets,  by  the  amount  of 
shearing  strain  allowed  on  each  unit,  equal  to  the  maximum 
strain  transmitted  through  the  joint. 

If  the  strain  was  one  of  compression  in  the  plates  and  the 
ends  exactly  fitted,  the  only  riveting  required  wrould  be  that 
necessary  to  keep  the  plates  in  position.  As  the  workman- 
ship rarely,  if  ever,  admits  of  so  exact  fitting,  the  rivets 
should  be  proportioned  by  the  rules  just  given. 

245.  The  head  of  a  rivet  is  usually  circular  in  form,  with 
a  diameter  not  less  than  twice  the  diameter  of  the  rivet. 

The  thickness  of  the  head  at  its  centre  should  be  not  less 
than  half  the  thickness  of  the  rivet. 


) 

ooioo 
ooioo 

O  OiOO 

< 

FIG.  53. 

^  246.  Various  methods  are  used  in  the  arrangement  of  the 
rivets.  The  arrangement  often  used  for  lengthening  a  plate 
is  shown  in  Fig. 53.  This  method  is  known  as  "chain  rivet- 
ing." 


ARRANGEMENT   OF   RIVETS. 


175 


Fig.  54  shows  another  method  used  for  the  same  purpose, 
in  which  the  number  of  rivets  is  the  same  as  in  the  previous 
example,  but  there  is  a  better  disposition  of  them. 


FIG.  54. 

Figs.  55  and  56  show  the  arrangement  of  the  rivets  often 
nsed  to  fasten  ties  to  a  plate. 


r 

0  0 

o  o 

000 
000 

o  o 

( 

/-v 

*"S, 

FIG.  55. 


FIG.  56. 


Figs.  57,  58,  and  59  show  in  plan  the  forms  of  several 
kinds  of  riveted  joints. 


FIG.  57. 


Fig.  57  shows  the  single  shear-joint  or  single  lap-joint. 


FIG.  58. 


Fig.  58  is  a  plain  joint  fished.     In  this  example  the  fish 
or  cover  plates  are  placed  on  each  side,  and  have  a  thick- 


176  CIVIL  ENGINEERING. 

ness  of  half  that  of  the  plates  to  be  connected ;  sometimes 
only  one  cover  plate  is  used. 


_s L 


v-       i 


FIG.  59. 


When  several  plates  are  to  be  fastened  together,  the  method 
shown  in  Fig.  59  is  the  one  ordinarily  used. 


Eye-bar  and  Pin  Joints. 

247.  A  simple  and  economical  method  of  joining  flat  bars 
end  to  end  when  subjected  to  a  strain  of  extension,  is  to  con- 
nect them  by  pins  passing  through  holes  or  eyes  made  in  the 
ends  of  the  bars. 

When  several  are  connected  end  to  end,  they  form  a  flexi- 
ble arrangement,  and  the  bars  are  often  termed  links. 

This  method  of  connecting  is  called  the  eye-bar  and  pin, 
or  link  and  pin  joint,  and  is  shown  in  plan  in  Fig.  60. 


PIG.  60. 

The  bar  should  be  so  tormed  at  the  end  that  it  would  be 
no  more  liable  to  break  there  than  at  any  other  point.  The 
following  are  the  dimensions  in  the  case  where  the  head  has 
the  same  thickness  as  the  bar. 

If  the  width  of  the  bar  be  taken  as  equal  to. 1 . 

The  diameter  of  the  eye  should  equal 75. 

Depth  of  head  beyond  the  eye  should  equal 1 . 

Sam  of  the  sides  of  the  head  through  eye  should  equal  1 .25. 

Radius  of  curve  of  neck  should  equal 1.5. 

Hence,  for  a  bar  eight  inches  wide,  the  dimensions  would 
be  as  shown  in  Fig.  61. 


SCREW-BOLTS. 


177 


By  this  rule  the  pin  has  a  diameter  which  gives  a  sufficient 
bearing  surfaee,  the  important  point  to  be  considered. 


FIQ.  61. 


There  should  be  a  good  fit  between  the  pin  and  eye,  espe- 
cially in  structures  subjected  to  shocks,  hence  the  conditions 
of  manufacture  and  the  quality  of  material  and  workmanship 
should  be  of  the  best  kind. 

Screw-bolt  Joints. 

248.  The  connection  by  nut  and  screw  is  simple  and 
economical. 

The  strength  of  a  bolt  or  rod  on  which  a  screw  is  made, 
when  subjected  to  a  shearing  strain,  is  determined  as  in  the 
case  of  rivets  or  pins.  In  case  of  a  tensile  strain  the  strength 
is  measured  by  the  area  of  cross-section  of  the  spindle  inside 
the  thread. 

The  resistance  offered  to  stripping  by  the  nut  depends  upon 
the  form  of  the  thread  and  the  depth  of  the  nut.  In  order 
that  this  resistance  should  be  equal  to  that  offered  by  the  bolt 
to  being  pulled  apart,  the  length  of  the  nut  should  be  at  least 
equal  to  one-half  the  diameter  of  the  screw. 

The  following  proportions  have  been  recommended  by  the 
Franklin  Institute : 


Diameter  of 

No.  of  threads 

Six-sided  nut.—  Length  of 

Depth  of 

Depth  of 

bolt  in  inches. 

per  inch. 

head. 

nut. 

Long  diameter, 

Short  diameter, 

i 

13 

1 

i 

ft 

4 

I 

10 

i-.V 

H 

* 

J 

8 

ii 

u 

H 

1 

H 

0 

2* 

8f 

1A 

14 

3 

4| 

a* 

84 

ift 

2 

»i 

4 

4* 

3i 

Itt 

9* 

84 

5| 

4| 

2A 

8 

178  CIVIL   ENGINEERING. 


SIMPLE  BEAMS. 

249.  One  of  the  most  common  and  simple  use  of  frame* 
is  that  in  which  the  frame  is  supported  at  its  extremities  and 
subjected  only  to  a  transverse  strain. 

When  the  distance  between  the  points  of  support,  or  the 
bearing,  is  not  very  great,  frames  are  not  necessary,  as  beams 
of  ordinary  dimensions  are  strong  and  stiff  enough  to  resist 
the  cross-strains  arising  from  the  load  they  support,  without 
bending  beyond  the  allowed  limits.  The  load  placed  upon 
them  may  be  uniformly  distributed,  or  may  act  at  a  point ; 
in  either  case  the  strains  produced,  and  the  dimensions  of  the 
beam  to  resist  them,  can  be  easily  determined.  (Arts.  177 
and  179.) 

The  usual  method  is  to  place  the  beams  in  parallel  rows, 
the  distances  apart  depending  on  the  load  they  have  to  sup- 
port. The  joists  of  a  floor,  the  rafters  of  a  roof,  are  exam- 
ples of  such  cases. 

The  depth  of  a  beam  used  for  this  purpose  is  always  made 
much  greater  than  its  breadth,  and  arrangements  should  be 
made  to  prevent  the  beam  twisting  or  bending  laterally.  It 
is  usual  to  place  short  struts  or  battens  in  a  diagonal  direction 
between  the  joists  of  a  floor,  fastening  the  top  of  one  joist 
with  the  bottom  of  the  next  by  the  battens  to  prevent  them 
from  twisting  or  yielding  laterally. 


SOLID  BUILT  BEAMS. 

250.  A  solid  beam  is  oftentimes  required  to  be  of  a 
greater  size  than  that  possessed  by  any  single  piece  of  tim- 
ber. To  provide  such  a  beam  it  is  necessary  to  use  a  com- 
bination of  pieces,  consisting  of  several  layers  of  timber  laid 
in  juxtaposition  and  firmly  fastened  together  by  bolts,  straps, 
or  other  means,  so  that  the  whole  shall  act  as  a  single  piece. 
This  is  termed  a  solid  built  beam. 


FIG.  62. 

"When  two  pieces  of  timber  are  built  into  one  beam  having 
twice  the  depth  of  either,  keys  of  hard  wood  are  used  to  resist 
the  shearing  strain  along  the  "joint,  as  shown  in  Fig.  62. 


SOLID   BUILT  BEAMS. 


179 


Tredgold  gives  the  rule  that  the  breadth  of  the  key  should 
be  twice  its  depth,  and  the  sum  of  the  depths  should  be  equal 
to  once  and  a  third  the  total  depth  of  the  beam. 

It  has  been  recommended  to  have  the  bolts  and  the  keys  on 
the  right  of  the  centre  make  an  angle  of  45°  with  the  axis  of 
the  beam,  and  those  on  the  left  to  make  the  supplement  of 
this  angle. 

The  keys  are  sometimes  made  of  two  wedge-shaped  pieces 
(Fig.  63)/for  the  purpose  of  making  them  fit  the  notches 


FIG.  63— Represents  the  folding  wedges,  a,  J,  let  into  a  notch  in 
the  beam  c. 

more  snugly,  and,  in  case  of  shrinkage  in  the  timber,  to  allow 
of  easy  readj  ustment. 

When  the  depth  of  the  beam  is  required  to  be  less  than  the 
sum  of  the  depths  of  the  two  pieces,  they  are  often  built  into 
one  by  indenting  them,  the  projections  of  the  one  fitting 
accurately  into  the  notches  made  in  the  other,  the  two  being 
firmly  fastened  together  by  bolts  or  straps.  The  built  beam 
shown  in  Fig.  64  illustrates  this  method.  In  this  particular 
example  the  beam  tapers  slightly  from  the  middle  to  the 
ends,  so  that  the  iron  bands  may  be  slipped  on  over  the  ends 
and  driven  tight  with  mallets. 


FIG.  64— Represents  a  solid  bnilt  beam,  the  top  part  being  of  two  pieces,  b,  b, 
which  abut  against  a  broad  flat  iron  bolt,  a,  termed  a  king-bott. 

When  a  beam  is  built  of  several  pieces  yi  lengths  as  well 
as  in  depth,  they  should  break  joints  with  each  other.  The 
layers  below  the  neutral  axis  should  be  lengthened  by  the 
scarf  or  fish  joints  used  for  resisting  tension,  and  the  upper 


180 


CIVIL   ENGINEERING. 


ones  should  have  the  ends  abut  against  each  other,  using  plain 
butt  joints. 

Many  builders  prefer  using  a  built  beam  of  selected  tim- 
ber to  a  single  solid  one,  on  account  of  the  great  difficulty  of 
getting  the  latter,  when  very  large,  free  from  defects ;  more- 
over, the  strength  of  the  former  can  be  relied  upon,  although 
it  cannot  be  stronger  than  the  corresponding  solid  beam  if 
perfectly  sound. 


FRAMING   WITH   INTERMEDIATE   POINTS    OF    SUPPORT. 

251.  If  the  bearing  be  great,  the  beam  will  bend  under 
the  load  it  has  to  support,  and  to  prevent  this  it  will  need  in- 
termediate points  of  support.  These  points  of  support  may 
be  below  the  beam,  or  they  may  be  above  it. 

The  simplest  method,  when  practicable,  is  to  place  at  suit- 
able intervals  under  the  beam  upright  pieces  to  act  as  props 
or  shores. 

When  this  cannot  be  done,  but  points  of  support  can  be 
obtained  below  those  on  which  the  beam  rests,  inclined  struts 
may  be  usjed. 

These  may  meet  at  the  middle  point  of  the  beam,  divid- 
ing it  into  two  equal  parts.  The  beam  is  then  said  to  be 
braced,  and  is  no  longer  supported  at  two  points,  but  rests 
on  three. 

The  struts  may  be  placed  so  as  to  divide  the  beam  (Fig.  65) 
into  three  parts,  being  connected  with  it  by  suitable  joints. 


FIG.  65. 


The  bearing  of  the  beam  may  be  reduced  by  placing  under 
it  and  on  the  points  of  support  (Fig.  66)  short  pieces,  termed 
corbels.  These,  when  long,  should  be  strengthened  by  struts, 
as  shown  in  the  figure. 

In  some  cases  the  beam  is  strengthened  by  placing  under 


OPEN-BUILT   BEAMS.  181 

the  middle  portion  a  short  piece,  termed  a  straining  beam 

(Fig.  67),  which  is  supported  by  struts. 


FIG.  66 — A  horizontal  beam,  e,  resting  on  vertical  posts,  a  a,  with 
corbels,  d  d,  and  struts,  e  e. 

These  methods  may  be  combined  when  circumstances  re- 
quire it,  and  the  strains  on  the  different  parts  can  be  deter- 
mined. It  is  well  to  remember  that  placing  equal  beams  over 


FlG.  67— A  horizontal  beam,  e,  strengthened  by  a  straining  beam,  /. 

each  other  only  doubles  the  strength,  unless  they  are  firmly 
connected  so  as  to  act  as  one  beam,  in  which  case  the  combi- 
nation follows  the  law  already  deduced,  that  is,  the  strength 
will  be  four  times  as  great. 


OPEN-BUILT  BEAMS. 

252.  An  open-built  beam,  or  truss,  is  a  frame  in  which 
two  beams,  either  single  or  solid  built,  with  openings  between 
them,  are  connected  by  cross  and  diagonal  pieces,  so  that  the 
whole  arrangement  acts  like  a  single  beam  in  receiving  and 
transmitting  strains. 

These  frames  are  largely  used  in  bridge  building,  and  their 
details  will  be  considered  under  that  head. 

The  king-post  truss  is  one  of  the  simplest  forms  of  frames 
belonging  to  this  class. 

This  truss  is  employed  when  there  are  no  points  ot  support 
beneath  the  beam  which  can  be  used,  but  when  the  middle  of 
the  beam  can  be  sustained  by  suspension  from  a  point,  above. 

The  arrangement  consists  of  two  inclined  pieces  framed 


182 


CIVIL   ENGINEERING. 


into  the  extremities  of  the  beam,  and  meeting  At  an  angle 
above,  from  which  the  middle  of  the  beam  is  ^  supported  by  a 
third  piece.  This  combination  is  shown  in  Fig.  68. 


FIG.  68. 

The  construction  is  simple  and  the  frame  is  rigid.  It  is 
frequently  employed  in  roofs  and  in  bridges  of  short  span. 

In  the  earlier  constructions  the  third  piece,  <?,  was  made  of 
wood,  and  resembled  a  post,  hence  the  name  of  king-post. 
The  strain  it  sustains  is  one  of  tension,  and  in  modern  con- 
structions an  iron-rod  is  generally  used.  It  would  be  better 
if  a  more  appropriate  name  were  given,  since  the  term  post 
conveys  to  the  mind  an  impression  that  the  strain  is  one  of 
compression. 

When  the  suspension  piece  is  made  of  timber,  it  may  be  a 
single  piece  framed  into  the  struts,  and  the  foot  connected 
with  the  beam  by  a  bolt,  an  iron  stirrup,  or  by  a  mortise  and 
tenon  joint ;  or  it  may  be  composed  of  two  pieces  bolted 
together,  embracing  the  heads  of  the  struts  and  the  supported 
beam.  In  the  latter  case,  these  pieces  are  called  bridle- 
pieces,  two  of  which  are  shown  in  Fig.  69. 


FIG.  69. 


When  two  points  of  support  are  necessary,  the  arrangement 
known  as  the  queen-post  truss  may  be  used.  It  consists  of 
two  struts  framed  into  the  extremities  of  the  beam,  and  abut- 
ting against  a  short  straining  beam  (Fig.  69).  The  suspen- 


8TEAJNS    ON   FRAMES.  183 

sion  pieces  are  either  of  iron  or  wood,  single  or  double,  as  in 
the  king-post  truss. 

The  remarks  just  made  about  the  name  "post"  apply  also 
to  this  combination. 

Both  of  these  trusses  may  be  inverted,  thus  placing  the 
points  of  support  beneath  the  beam.  This  change  of  position 
changes  the  character  of  strains  on  the  different  parts,  but 
does  not  affect  their  amount,  which  is  determined  in  the  same 
way  in  both  cases. 

Points  of  support  above  and  beneath  may  be  obtained  by 
the  use  of  curved  beams. 


METHODS  OF  CALCULATING  STRAINS  ON  FRAMES. 


253.  It  has  been  previously  stated  that  to  prevent  a  change 
of  form  in  a  quadrilateral  frame,  secondary  pieces  are  intro- 
duced for  the  purpose  of  dividing  the  frame  into  two  or  more 
triangular  figures. 

In  all  frames  "where  rigidity  is  essential  to  stability,  this  in- 
troduction of  braces  is  necessary,  as  the  triangle  is  the  only 
geometrical  figure  which,  subjected  to  a  straining  force, 
possesses  the  property  of  preserving  its  form  unaltered  as 
long  as  the  lengths  of  its  sides  remain  constant. 

The  triangular  is  the  simplest  form  of  frame,  and  will  be 
first  used  in  this  discussion. 

254.  As  a  preliminary  step,  let  the  strains  in  an  inclined 
beam,  arising  from  a  force  acting  in  the  plane  of  its  axis,  be 
determined. 

For  example,  take 

An  inclined  beam  with  the  lower  end  resting  against  an 
abutment  and  the  upper  end  against  a  vertical  watt,  and  sup- 
porting a  weight,  W,  applied  at  any  point. 

Fig.  70  represents  the  case. 

Denote  by 

Z,  the  length  of  the  axis,  A  B,  of  the  beam; 

n  x  I,  the  distance  from  A  to  the  point  C,  where  W  is  ap- 
plied ; 

a,  the  angle  between  A  B,  and  vertical  line  through  C. 

Disregarding  the  weight  of  the  beam,  the  external  forces 
acting  on  it  are  the  weight,  W,  and  the  reactions  at  A  and  B. 

Suppose  the  reaction  at  B  to  be  horizontal  and  represent 
it  by  H.  Kepresent  the  horizontal  and  vertical  components 
of  the  reaction  at  A,  respectively  by  H'  and  W. 


184: 


CIVIL   ENGINEERING. 


These  forces  are  all  in  the  same  plane,  and  the  analytical 
conditions  for  equilibrium  are 

H  -  H'  =  0,  and  W  -  W  =  0. 


If 


w 


FIG.  70. 

Taking  the  bending  moment  about  A,  we  have 

WxAD-HxBE  =  0, 
or,                     H  x  I  cos  a  =  W  x  nl  sin  a, 
hence,  H  =  n  W  tan  a 

The  forces  H,  IF,  W,  and  W  act  in  the  plane  of  and 
obliquely  to  the  axis,  A  B,  and  their  effect  is  to  produce  de- 
flection and  compression  of  the  fibres  of  the  beam.  The 
strain  arising  from  deflection  will  be  due  to  the  algebraic  sum 
of  the  perpendicular  components,  and  that  from  compression 
will  be  due  to  the  sum  of  the  parallel  ones.  (Art.  217.) 

Resolve  W  and  H'into  components  acting  perpendicularly 
and  parallel  to  the  axis  of  the  beam.  Represent  by  P  and 
P',  and  Q  and  Q',  these  components;  see  Fig.  71. 


kd 


=  W  =  W. 

=.P,  Ac  =  Q. 

=  H'  =  nW  tan  a. 

=  P',  Aw  =  Q'. 


STRAINS   ON   FRAMES. 


185 


The  perpendicular  components  kd  and  km  act  in  opposite 
directions,  hence  the  strain  arising  from  deflection  will  be  due 
to  their  difference,  P  —  P'. 


FIG.  71. 


The  parallel  components  kc  and  kn  act  in  the  same  direc- 
tion, hence  the  strain  of  compression  will  be  due  to  their  sum, 
Q  +  Q'. 

Representing  the  force  W,  by  the  line  A5,  we  find  the  values 
of  these  components  to  be  as  follows : 

P  =  W  sin  a ;  P'  =  n  W  tan  a  cos  a  =  n  W  sin  a; 
Q  =  W  cos  a ;  Q'  =  n  W  tan  a  sin  a. 

Suppose  the  cross-section  of  the  beam  to  be  a  rectangle  of 
uniform  dimension,  the  sides  of  which  are  respectively  b 
and  d,  the  plane  of  the  latter  being  taken  parallel  to  the 
direction  of  the  force,  W,  we  have 

Q  4.  Q'  =  W  cos  a  +  n  W  tan  a  sin  a, 

equal  to  the  total  compression  on  the  segment  from  A  to  C ; 
this  sum  divided  by  bd  will  be  the  amount  of  compression 
on  the  unit  of  area  in  any  cross-section  in  this  segment. 
We  also  have 

P  -  P'  =  (1  -  n)  W  sin  a, 

for  the  force  perpendicular  to  the  axis  of  the  beaml  Ita 
moment  for  any  section,  at  the  distance,  a?,  measured  on  the 
line  A  B,  and  lying  between  A  and  C,  will  be 

(1  —  n)  W  sin  a  x  «. 


186  CIVIL   ENGINEERING. 

Substituting  in  the  expression  for  R.'  (Art.  206),  we  have 

(1  _  ri\  Wo?  sin  a 
-/      \ 


for  the  stress  on  the  unit  of  area  farthest  from  the  neutral 
axis  in  any  section  produced  by  deflection,  x  being  the  lever 

arm 

For  the  segment  of  the  beam,  B  C,  it  is  seen  that  the  strain 
of  direct  compression  is  due  to  the  force 

Q'  =  n  W  tan  a  sin  a. 

Giving  values  to  ^,  from  0  to  1,  we  can  place  the  force,  W, 
at  any  point  on  the  axis.  And  knowing  5,  d,  and  W,  and 
substituting  them  in  the  foregoing  expressions,  we  obtain  the 
stresses  in  the  beam. 

Let  us  place  it  at  the  middle  point,  arid  suppose  W  and  a  to 
be  given. 

The  value  of  n  for  the  middle  point  is  £;  substituting  which 
in  the  expressions  for  P,  Q,  etc.,  there  obtains : 

W  cos  a  4-  iW  tan  a  sin  a 


for  the  stress  of  compression  on  the  unit  of  cross-section  ;  and 
(P  —  P'fe  _     JW  x  sin  a 


for  the  stress  due  to  deflection  on  the  unit  of  cross-section 
farthest  from  the  neutral  axis.  Represent  these  by  C'  and  R', 
respectively.  To  determine  the  greatest  stress  on  the  unit  of 
area  in  any  cross-section  ;  first,  determine  R/  for  the  particu- 
lar section  and  add  to  the  value  thus  found  that  for  C',  and 
the  result  will  be  the  total  stress  on  the  unit,  and  hence  the 
maximum  stress  in  that  section. 

To  determine  the  greatest  stress  produced  by  the  force, 
W,  upon  the  unit  of  surface  of  the  beam  :  first,  find  the  value 
of  R'  for  the  dangerous  section  and  then  add  to  it  the  value 
of  C'  for  this  section  ;  the  result  will  be  the  greatest  stress. 

Assuming  limiting  values  for  R'  and  C'and  knowing  &  and 
d,  the  corresponding  value  for  "W"  can  be  deduced.  Or,  as- 
suming R'  and  C'  and  having  "W  given,  we  can  deduce  values 
for  ~b  and  d. 

Suppose  the  beam  to  be  vertical,  then  a  =  0,  and  we  get 

Q  =  W,  and  Q'  =  0, 


STRAINS   ON   FRAMES  187 

or  the  compression  in  B  C  will  be  zero,  and  on  A  C  equal  to 
W.  "We  also  have  H'  =  0,  or  there  is  no  horizontal  thrust. 

Suppose  the  beam  horizontal,  then  a  =  90°,  and  we  get  IF 
and  Q',  each  equal  to  infinity. 

From  this  it  is  seen  that  the  compression  on  the  beam  and 
the  horizontal  thrust  at  the  foot  both  decrease  as  a  decreases, 
and  the  reverse. 

255.  Uniformly  loaded. — Suppose  the  beam  to  be  uni- 
formly loaded,  and  let  w  be  the  load  on  a  unit  of  length  of 
the  beam. 

We  have  H  =  \wl  tan  a. 

The  corresponding  values  for  P,  P',  Q,  and  Q'  are  easily 
obtained. 

256.  Let  it  be  required  to  determine  the  strains  on  a 
triangular  frame,  and  take  for  example, 

A  frame  made  of  three  beams  connected  at  the  ends  by 
proper  joints  and  strained  by  a  force  acting  in  the  plane  of 
their  axes  and  at  one  of  the  angular  points. 

Suppose  the  plane  of  the  axes  ofc  the  three  beams  to  be  ver- 
tical, and  one  of  the  sides,  B  C,  to  be  horizontal,  resting  on 
fixed  points  of  support  at  B  and  C. 

Disregarding  the  weight  of  the  frame  itself,  suppose  the 
straining  force  to  be  a  weight  suspended  from  or  resting  on 
the  point  A.     (Fig.  72.) 
Represent  by 

"W,  the  weight  acting  at  A, 
a,  the  angle  BAD, 
«      "     CAD. 


FIG.  72. 


The  weight,  W,  acts  vertically  downwards  and  is  prevented 
from  falling  by  the  support  at  A.  The  pressure  exerted  by 
it  at  A  is  received  by  the  inclined  beams,  A  B,  and  A  C,  and  is 
transmitted  by  them  to  the  fixed  points  of  support  at  B  and  C. 


188  CIVIL   ENGINEERING. 

The  weight,  W,  is  therefore  the  resultant  force  acting  on  the 
frame,  and  the  pressure  on  the  inclined  beams  are  its  compo- 
nents in  the  directions  of  the  axes  of  the  beams. 

Kepresent  by  kd  the  weight  W,  and  construct  the  parallelo- 
gram kbcd.  We  have  from  the  principle  of  the  parallelo- 
gram of  forces  : 

Wsin£  Wsina 

M>  =   -    f     .   Q\   and  Ac  =  '•    t    -L/QV 
sin  (a  +  p)  sin  (a  +  p) 

The  strains  produced  by  these  components  are  compressive. 
Knowing  the  breadth  and  depth  of  the  beams,  the  amount  of 
stress  on  the  unit  of  cross-section  can  be  determined  ;  or 
assuming  a  limit  for  this  stress  on  the  unit,  the  values  for  the 
breadth  and  depth  of  the  beams  may  be  deduced. 

These  components  being  transmitted  along  the  axes  of  the 
beams  to  the  points  of  support,  B  and  C,  may  be  resolved  at 
these  points  into  their  horizontal  and  vertical  components 
respectively. 

Doing  so,  it  is  seen  that  the  horizontal  components  are 
equal  to  bm  and  en,  and  are  equal  to  each  other,  but  act  in 
opposite  directions.  The  value  for  these  components  is 


.  (126) 

Hence,  they  balance  each  other,  producing  a  strain  of  ex- 
tension on  the  beam,  B  C,  the  amount  of  which  on  the  unit  of 
cross-section,  or  dimensions  of  beam  to  resist  which,  may  be 
determined.  The  vertical  components  are  respectively  equal 
to  Am  and  kn,  and  act  in  the  same  direction.  We  have 

_  sin  /3  cos  a  _  sin  a  cos  8   . 

Am  =  W  .    ,     ,  ^  and  kn  =  W  -r-,  —  r-~.  (12T) 
sm(a  +  £)'  sin  (a  +  /3)  v      ' 


They  are  resisted  by  the  reactions  at  the  points  of  support, 
which  must  be  strong  enough  to  sustain  these  vertical  pres- 
sures. Adding  Am  to  kn  we  find  their  sum  is  equal  to  W. 
It  is  well  to  observe  that  producing  kd  to  D,  we  have  the  pro- 
portion, Am  :  ATI  :  :  C  D  :  B  D.  That  is,  the  vertical  through  A 
divides  the  side  B  C  into  two  segments  proportional  to  the 
vertical  components  acting  at  B  and  C. 

257.  The  common  roof-truss,  in  which  A  B  is  equal  in 
length  to  A  C,  and  the  angle  a  equal  to  ft,  is  the  most  usual 
form  of  the  triangular  frame. 


STRAINS   ON   FRAMES.  189 


For  this  case  we  would  have 

W 

A5  =  kc  —  -J  -  -  ,  lm  =  £W  tan  a,  and  km  =  ATI  =  \  W. 


COS  CL 


Kepresent  by  21  the  length  of  B  C,  d,  the  length  of  A  D 
and  A,  the  length  of  A  B  =  A  C,  and  substituting  in  the  fore- 
going expression,  we  have 


=  en  =          , 

which  are  fully  given  for  any  assumed  value  for  W  when 
either  two  of  the  quantities  in  the  second  members  are 
known. 

If,  instead  of  a  single  weight,  the  frame  had  been  strained 
by  a  uniform  load  distributed  over  the  inclined  pieces  A  B 
and  A  C,  we  may  suppose  the  whole  load  to  be  divided  into 
two  equal  parts,  one  acting  at  the  middle  point  of  A  B  and 
the  other  at  the  middle  point  of  A  C,  the  discussion  of  which 
would  have  been  similar  to  that  of  the  previous  article. 

If  the  frame  be  inverted  (Fig.  73)  the  method  of  calculat- 
ing the  strains  will  be  the  same.  Under  this  supposition  the 


W 
FIG.  78. 

strains  in  the  inclined  pieces  will  be  tensile  instead  of  com- 
pressive,  and  in  the  horizontal  piece  B  C  will  be  compressive 
instead  of  tensile,  the  expression  for  the  intensities  remaining 
the  same. 

258.  The  jib-crane. — The  machine  known  as  the  jib- 
crane,  which  is  used  for  raising  and  lowering  weights,  is  an 
example  of  a  triangular  frame.  Its  principal  parts  are 
a  vertical  post,  B  C  ;  a  strut,  A  C ;  and  an  arm  or  tie-bar,  A  P. 
(Fig.  74.) 

Ordinarily,  the  whole  frame  allows  a  motion  of  rotation 
around  the  vertical  axis,  B  C. 


190 


CIVIL   ENGINEERING. 


The  weight,  W,  suspended  from  the  frame  at  A  is  kept 
from  falling  by  resistances  acting  in  the  directions  A  B  and 
A  C.  There  being  an  equilibrium  of  forces  at  A,  the  resultant, 
W,  and  the  direction  of  the  resistances  being  known,  the  in- 
tensities of  these  resistances  are  easily  determined. 


w 


FIG.  74. 


JRepresent  W  by  kd,  and  construct  the  parallelogram  kbdc. 
kl  and  kc  will  represent  the  intensities  of  the  forces  acting  to 
keep  W  from  falling. 
From  the  parallelogram  we  have 


ko  —  W 


sin  /3 


sin  (a  + 


.     .    (128) 


which,  as  it  is  seen,  produces  compression  on  the  strut  A  C, 
and  a  transverse  shearing  strain  at  C  on  the  post  C  B.  The 
horizontal  component  of  A  C  divided  by  the  area  of  cross- 
section  of  the  post  B  C,  gives  the  shearing  stress  on  the  unit 
of  cross-section  at  C. 


We  also  have        A5  =  W 


sm  a 


sin  (a  +  /3)' 


for  the  stress  acting  in  the  direction  of  A  B,  tending  to  elon- 
gate it,  and  to  produce  a  cross-strain  on  B  C.  The  greatest 
bending  moment  is  at  C.  Knowing  the  stresses,  it  is  a  simple 
problem  to  proportion  the  pieces  so  that  the  crane  may  be 
able  to  lift  a  given  weight,  or  to  determine  the  greatest 
weight  which  a  given  crane  may  lift  with  safety. 


TRIANGULAR   BRACING. 


191 


COMBINED   TRIANGULAR  FRAMES. 

259.  Open-built  beams  constructed  by  connecting  the  uppe" 
and  lower  pieces  by  diagonal  braces  are  examples  of  com 
binations  of  triangular  frames. 

Triangular  Bracing. 

260.  Triangular  bracing  with  load  at  free  end.— Take 
a  beam  of  this  kind  and  suppose  it  placed  in  a  horizontal 
position,  one  end  firmly  fixed,  the  other  free  to  move,  and 
strained  by  a  force  acting  at  the  free  end.     Suppose  the  tri- 
angles formed  by  the  braces  to  be  equilateral  (Fig.  75)  and 
disregard  the  weight  of  the  beam. 


*    £ 


FIG,  75. 

Represent  by  "W  the  force  acting  at  A,  in  the  plane  of  the 
axes  of  the  pieces  of  the  frame  and  perpendicular  to  A  G. 

The  force  W  acting  at  A  is  supported  by  the  pieces  A  B 
and  A  A',  and  produces  a  stress  of  compression  in  A  A'  and 
tension  in  A  B.  Laying  off  on  A  W  the  distance  kd  to  repre- 
sent W,  and  constructing  the  parallelogram  kbcd,  we  have  Ac 
and  ko  representing  the  intensities  of  these  stresses. 

From  the  parallelogram  there  results 

W 

kc~  -  — ,        and        kb  =  W  tan  a. 
cos  a' 

The  compressive  force  Ac  is  transmitted  to  A'  and  there 
supported  by  the  pieces  A'B  and  A'B'.  Resolving  this  force 
at  A'  into  its  components  acting  in  the  directions  of  A'B  and 
A'B',  we  have  k'd'  =  2Wtan  a,  which  produces  compression 

W 

in  A'B'.  and  k'b'  =  -  — .  which  produces  tension  in  A'B. 
cos  a' 

This  tension  A'  I'  is  transmitted  by  the  brace  to  B.     Re- 


192  CIVIL   ENGINEERING. 

solving  it  into  its  components  in  the  directions  B  B'  and  B  C, 
we  have 

Compression  on  B  B'  =  ^-^, 

Tension  on  B  C  =  2W  tan  a. 

The  tension  at  A  is  transmitted  through  the  beam  to  B, 
hence  the  tension  at  B  is  equal  to  the  sum  of  them,  or 

Tension  at  B  =  2W  tan  a  +  W  tan  a  =  3W  tan  a. 

Continuing  this  process,  we  find  that  the  force  W,  strains 
all  the  diagonals  equally,  but  by  forces  which  are  alternately 
compressive  and  tensile,  and  the  expression  for  which  is 

.    In  this  case  the  braces  numbered  odd  in  the  figure  are 

cos  a 

compressed,  and  those  even  are  extended. 

The  stresses  in  the  upper  and  lower  beams  are  cumulative, 
receiving  equal  increments,  each  equal  to  2W  tan  a,  at  each 
point  of  junction  of  the  brace  with  the  beam.  Hence,  in  this 
case,  for  the  upper  beam  we  have 

W  tan  a  for  A  B,  3  W  tan  a  for  B  C,  5W  tan  a  for  C  D,  etc., 
and  for  the  lower, 
2W  tan  a  for  A'B',  4W  tan  a  for  B'C',  6 W  tan  a  for  C'D',  etc. 

Having  determined  the  stresses  in  the  different  parts  of 
the  frame  produced  by  a  force  "W",  it  is  easy  to  find  the 
greatest  weight  that  such  a  frame  will  support,  or  to  propor- 
tion its  different  parts  to  resist  the  strains  produced  by  a  given 
load. 

The  triangles  taken  were  equilateral.  If  we  denote  by  d 
the  altitude  E'o?  of  one  of  these  triangles,  or  depth  of  the 
beam ;  by  Z,  the  length  of  one  of  the  sides  F  E,  or  distance 
between  the  vertices  of  two  adjacent  triangles,  which  we  will 
call  a  bay ;  and  express  the  values  of  cos  a  and  tan  a  in  terms 

of  these ;  then  we  have  cos  a  =  , ,  and  tan  a  =  ^.  Substituting 
which  in  the  foregoing  expressions,  there  obtains  -rW  for  the 
stress  in  the  diagonal,  and,  -jW  for  the  increment  to  be 

Cu 

added  at  each  point  of  junction. 

To  find  the  stress  in  any  segment ;  as,  for  example,  L  F. 

The  tension  on  A  B  is  W  tan  a  =  /rjW,  to  which  add  four 


TEIAKGULAE   BRACING.  193 

equal  increments,  there  being  four  bays  between  A  and  the 
segment  E  F,  and  we  have,  for  the  tensile  stress  in  E  F, 

9£ 
9W  tan  a,  or  its  equal  ^W. 

261.  Triangular  Bracing  Strained  by  a  Uniform  Load. 

— Suppose  the  strains  on  the  same  beam  to  be  caused  by  a 
weight  uniformly  distributed  over  either  the  upper  or  lower 
beam  of  the  frame. 

Let  A  E  F  A7  (Fig  76)  be  an  open-built  beam  supporting  a 
load  uniformly  distributed  over  the  upper  beam  A  E. 

Denote  by  w  the  weight  distributed  over  any  one  segment. 

We  may,  without  material  error,  suppose  the  whole  load 
divided  into  a  number  of  equal  parts,  each  equal  to  that  rest- 
ing on  the  adjacent  half  segments,  acting  at  the  points  A,  B,  C, 
etc.,  where  the  braces  are  connected  with  the  beam,  A  E. 


Since  there  are  four  of  these  bays,  the  total  load  is  4w,  the 
action  of  which  may  be  considered  to  be  the  same  as  that 
produced  by  the  weight  w  acting  at  each  of  the  points  B,  C, 
and  D,  and  \w  at  A  and  E. 

The  strains  on  A  B,  A  A',  A'B,  and  A'B'  are  due  to  the  weight 

•5  acting  at  A,  and  are  determined  as  in  the  preceding  case. 

The  strains  on  B  C,  B  B',  B'  C,  and  B'C'  are  due  to  the  ac- 
tion of  the  weight  w  acting  at  B,  increased  by  the  strains  due 


w 


to  -Q-  acting  at  A. 

The  strains  on  the  remaining  parts  are  due  to  the  weight 
acting  at  each  vertex,  increased  by  those  transmitted  from  the 
points  to  the  right  of  them. 

Hence  it  is  seen  that  the  stresses  in  each  of  the  pieces  in 
any  pair  of  diagonals  are  equal  in  amount,  but  different  in 
kind,  and  increase  as  they  go  from  the  point  of  application  to 
the  points  of  support  for  each  set;  and*  that  the  stresses  in 
the  segments  of  the  upper  ond  lower  beams  increase  in  the 
same  (Erection.  The  rate  of  increase  can  be  easily  determined. 
13 


194  CIVIL   ENGINEERING. 


METHOD  OP  SECTIONS. 

262.  The  stresses  in  the  different  pieces  of  a  frame  may  be 
obtained  by  using  the  principle  of  moments,  or,  as  it  is  usu- 
ally called,  the  "  method  of  sections."    This  method  consists 
in  supposing  the  frame  to  be  divided  by  a  section  cutting  not 
more  than  three  pieces  of  the  frame,  and  taking  the  inter- 
section of  two  of  these  pieces  as  a  centre  of  moments. 

It  is  evident  that  the  stresses  in  the  two  pieces  passing 
through  the  centre  of  moments  will  have  no  moments  to  op- 
pose those  of  the  extraneous  forces  acting  to  turn  the  frame 
around  the  assumed  centre,  and  that  these  external  moments 
must  be  held  in  equilibrium  by  the  moment  of  the  stress  in 
the  third  piece.  If  the  moment  of  the  stress  in  the  third 
piece,  with  respect  to  the  assumed  centre,  be  placed  equal  to 
the  bending  moment  of  the  extraneous  forces  with  respect 
to  the  same  point,  an  equation  will  be  found  that  must  be 
true  for  equilibrium,  and  which,  when  solved,  will  give  the 
intensity  of  the  stress  in  the  third  piece  whenever  the  posi- 
tion of  this  piece  and  the  bending  moments  are  known. 

Let  it  be  required  to  find  by  this  method  the  stress  in  the 
segment  E  F  (Fig.  75). 

Intersect  the  frame  by  a  vertical  plane  perpendicular  to  the 
axis  between  x  and  E,  and  let  T'  be  the  stress  in  the  piece 
E  F.  This  plane  will  cut  the  pieces  E  F,  E  E',  and  E'  D',  and 
Do  others.  Assume  E'  to  be  the  centre  of  moments. 

The  resultant  of  the  stress  T'  is  supposed  to  act  along  the 
axis  of  the  piece  F  E.  Its  moment  with  respect  to  E'  will  be 
T'  X  E'x. 

Since  there  is  an  equilibrium, 

T'  x  E'x  =  W  x  Aa>,  or,  T'  x  d  =  W  x  4|Z;  hence 
T'  =  4J-T  W,  the  same  value  before  deduced. 

In  a  similar  manner,  assuming  E  as  a  centre,  the  intensity 
of  the  stress  in  E'  D'  may  be  obtained. 

This  method,  in  many  cases,  is  a  convenient  one  and  its 
use  is  simply  a  matter  of  choice. 

Vertical  and  Diagonal  Bracing. 

263.  Suppose  the  triangles,  instead  of  being  equilateral, 
to  be  right-angled,  as  in  Fig.  77,  and  the  beam^strained  by  a 
load,  W,  as  in  the  preceding  case. 

The  stresses  in  the  upper  and  lower  beams  would  be  re- 


VERTICAL   AND   DIAGONAL    BRACING. 


195 


spectively  tensile  and  compressive,  and  cumulative  as  in  the 
preceding  case. 


The  expression  for  the  equal  increment  would  be 
Wtana. 

The  force  acting  on  the  diagonals  would  be  compressive 
and  equal  to 

W 

-  ,  same  as  in  preceding  case. 
cos  a' 

The  stress  in  the  verticals  would  be  tensile  and  equal  to 
W  for  each. 
Representing  by 

A,  the  length  of  a  diagonal,  A  A', 

I,  the  length  of  a  segment,  A  B, 

dy  the  length  of  a  vertical,  A'B,  we  can  write 


=  W-,  and 


cos 


d 


(129) 

^       ' 


expressions  more  frequently  used  when  calculating  the  stresses 
than  the  expressions  involving  the  circular  functions. 

If,  in  the  preceding  cases,  W  had  acted  in  the  opposite  di- 
rection, that  is,  pushed  the  point  A  upward  instead  of  pulling 
it  down,  or  the  same  thing,  the  frame  had  been  turned  over 
so  that  the  upper  beam  became  the  lower,  the  stresses  would' 
have  been  determined  in  the  same  manner  with  similai 
results,  excepting  that  the  inclined  pieces  would  have  been 
extended  instead  of  compressed,  and  the  verticals  compressed 
instead  of  extended. 


196 


CIVIL    ENGINEERING. 


ANGLE  OF  ECONOMY. 

264.  It  has  been  shown  that  the  stress  on  the  unit  of  cross- 
section  of  a  brace,  strained  by  a  force  as  W  (Fig.  77)  varies 
with  the  angle  made  by  the  brace  with  the  straining  force. 

It  is  plain  that  of  two  braces  of  the  same  material,  for  the 
same  stress  on  the  unit  and  the  same  span,  the  more  eco- 
nomical brace  will  be  the  one  that  contains  the  less  amount  of 
material ;  or,  for  the  same  stress  and  the  same  amount  of 
material,  the  one  that  gives  the  wider  span. 

Suppose  the  stress  on  the  unit  of  cross-section  and  the 
span  to  be  fixed,  it  is  required  to  find  the  angle  that  a  brace 
shall  make  with  the  straining  force  so  that  the  amount  of  ma- 
terial in  the  brace  shall  be  a  minimum. 

Let  B  C  be  the  fixed  span  (Fig.  78)  and  2W  the  intensity 
of  the  straining  force  acting  vertically  to  be  transmitted  by 
braces  to  the  points  B  and  C  considered  as  fixed.  Let  h  = 
the  length  of  A  B  =  A  C,  21  =  the  length  of  B  C,  and  d  =  the 
distance  A  D. 


FIG.  78. 


The  straining  force  produces  a  compressive  stress  in  each 
brace  equal  to  W—p 

Suppose  the  resistance  offered  by  the  brace  to  vary  directly 
with  the  area  of  its  cross-section  (Art.  164)  and  let  J2  be  the  area 
of  cross-section,  and  C',  the  assumed  compressive  stress  al- 
lowed on  the  unit.  We  can  then  form  the  following  equa- 
tion : 


. 
d 


=       x 


.    .    (130) 


from  which  we  obtain 


ANGLE   OF   ECONOMY.  197 

and 

W       A8 
tfh  =  —  x  -T,  for  the  volume  of  the  brace. 

Substituting  d*  -f  P  in  this  expression  for  7i2,  we  have 

Volume  of  brace  =  -777-  x  — -7 — •     •     •     •    (131) 
L»  # 

The  value  of  d  =  I  makes  this  function  a  minimum.  Hence, 
it  is  seen  that  the  volume  of  the  brace  is  a  minimum  when 
the  angle  which  it  makes  with  the  straining  force  is  equal 
to  45°.  This  angle  is  called  "  the  angle  of  economy "  of 
the  brace. 

In  this  discussion,  the  length  of  the  bay  or  span  has  been 
fixed.  A  similar  result  would  have  been  obtained  if  d,  the 
depth  of  the  truss,  had  been  fixed  and  the  length  of  the  bay 
B  C  determined. 

The  resistance  in  a  tie  to  tension  varies  directly  with  the 
area  of  cross-section,  however  long  the  piece  may  be,  and 
therefore  the  angle  above  obtained  is  the  true  angle  of  econ- 
omy for  ties  in  all  cases.  This  is  not  true  for  struts,  as 
experiment  has  shown  (Art.  202)  that  when  the  diameter  is 
small  in  comparison  to  its  length,  the  resistance  to  compres- 
sion becomes  also  a  function  of  its  length,  which  latter  di- 
mension must  be  duly  considered. 

The  angle  of  economy  for  a  strut  when  its  length  exceeds 
its  diameter  more  than  fifteen  or  thirty  times  can  be  deter- 
mined by  taking  the  formulas  deduced  from  Hodgkinson's 
experiments  for  finding  the  strength  of  pillars,  and  following 
the  steps  just  described. 

Merrill,  in  his  "  Iron  Truss  Bridges,"  gives  the  angle  of 
economy  for  a  cast-iron  strut  in  a  triangular  frame  at  27°  51', 
or  the  depth  of  the  frame  to  be  a  little  greater  than  one-fourth 
of  the  span.  In  diagonal  bracing  with  vertical  ties  (Art.  236) 
he  gives  the  angle  of  economy  for  the  struts  to  be  39°  49' 
with  the  vertical. 


PART   IV 

MASONRY. 


CHAPTER  IX. 


Masonry  is  the  art  of  erecting,  structures  in  stone, 
brick,  and  mortar. 

It  is  classified,  from  the  nature  of  the  material  used,  into 
stone,  brick,  and  mixed  masonry ;  from  the  manner  in  which 
the  material  is  prepared,  into  cutstone,  ashlar,  rubble,  and 
hammered  masonry ;  and  from  the  mode  of  laying  the 
blocks,  into  irregular  and  regular  masonry. 


MASONRY  STRUCTURES. 

266.  Masonry  structures  are  divided  into  classes  accord- 
ing to  the  kind  of  strains  they  are  to  sustain.  Their  forms 
and  dimensions  are  determined  by  the  amount  and  kind  of 
strains  they  are  required  to  resist.  They  may  be  classed  as 
follows : 

1st.  Those  which  sustain  only  their  own  weight ;  as  walls 
of  enclosures. 

2d.  Those  which,  besides  their  own  weight,  are  required  to 
support  a  vertical  pressure  arising  from  a  weight  placed  upon 
them ;  as  the  walls  of  a  building,  piers  of  arches,  etc. 

3d.  Those  which,  besides  their  own  weight,  are  required  to 
resist  a  lateral  thrust ;  as  a  wall  supporting  an  embankment, 
reservoir  walls,  etc. 

4th.  Those  which,  sustaining  a  vertical  pressure,  are  sub- 
jected to  a  transverse  strain  ;  as  lintels,  areas,  etc. 

5th,  Those  which  are  required  to  transmit  the  pressure  they 
directly  receive  to  lateral  points  of  support;  as  arches. 


EETAINING  WALLS.  190 


WALLS. 

267.  Definitions. — In  a  wall  of  masonry  the  front  is  called 
the  face  ;  the  inside  or  side  opposite,  the  back ;  the  layer  of 
stones  which  forms  the  front  is  called  the  facing,  and  that  of 
the  back,  the  "backing ;  the  portion  between  these,  forming 
the  interior  of  the  wall,  the  filling. 

If  a  uniform  slope  is  given  to  the  face  or  back,  this  slope  is 
termed  the  batter. 

The  section  made  by  a  vertical  plane  passed  perpendicular 
to  the  face  of  the  wall  is  called  the  profile. 

Each  horizontal  layer  of  stone  in  the  wall  is  called  a  course ; 
the  upper  surface  of  the  stone  in  each  course,  the  bed  or 
build;  and  the  surfaces  of  contact  of  two  adjacent  stones, 
the  joints. 

When  the  stones  of  each  layer  are  of  equal  thickness 
throughout,  the  term  regular  coursing  is  applied ;  if  un- 
equal, irregular  or  random  coursing.  The  particular  ar- 
rangement of  the  different  stones  of  each  course,  or  of  con- 
tiguous courses,  is  called  the  bond. 

Walls. — The  simplest  forms  of  walls  are  those  generally 
used  to  form  an  inclosing  fence  around  a  given  area,  or  to 
form  the  upright  inclosing  parts  of  a  building  or  room. 


RETAINING  WALLS. 

268.  A  retaining  -wall  is  the  term  used  to  designate  a 
wall  built  to  support  a  mass  of  earth  in  a  vertical  position,  or 
one  nearly  so.  The  term  sustaining  is  sometimes  applied  to 
the  same  case.  In  military  engineering,  the  term  revetment 
wall  is  frequently  used  to  designate  the  same  structure. 

The  earth  sustained  by  a  retaining  wall  is  usually  deposited 
behind  and  against  the  back  after  the  wall  is  built.  If  the 
wall  is  built  against  the  earth  in  its  undisturbed  position,  as 
the  side  of  an  excavation  or  cutting,  it  is  called  a  face-wall, 
and  sometimes  breast-wall. 

Reservoir  walls  and  dams  are  special  cases  of  retaining 
walls,  where  the  material  to  be  supported  is  water  instead  of 
earth. 

Counterforts  are  projections  from  the  back  of  a  retaining 
wall,  and  are  added  to  increase  its  strength.  The  projections 
from  the  face  or  the  side  opposite  to  the  thrust  are  called 
buttresses. 


20U 


CIVIL   ENGINEERING. 


AREAS,  LINTELS,  AND  PLATE-BANDS. 

269.  The  term  area  is  applied  to  a  mass  of  masonry,  usually 
of  uniform  thickness,  laid  over  the  ground  enclosed  by  the 
foundations  of  walls. 

The  term  lintel  is  applied  to  a  single  stone,  spanning  an 
interval  in  a  wall ;  as  over  the  opening  for  a  window,  door,  etc. 

The  term  plate-band  is  applied  to  the  lintel  when  it  is 
composed  of  several  pieces.  The  pieces  have  the  form  of 
truncated  wedges,  and  the  whole  combination  possesses  the 
outward  appearance  of  an  arch  whose  under  surface  is  plane 
instead  of  being  curved. 


ARCHES. 

270.  An  arch  is  a  combination  of  wedge-shaped  blocks, 
called  voussoirs  or  arch-stones,  supporting  each  other  by 
their  mutual  pressures,  the  combination  being  supported  at 
the  two  ends.  (Fig.  79.) 

These  blocks  are  truncated  towards  the  angle  of  the  wedges 
by  a  curved  surface,  generally  normal  to  the  joints  between 
the  blocks. 

The  supports  against  which  the  extreme  voussoirs  rest  are 
generally  built  of  masonry. 


c 

—  *^ 

/                              \ 

L 

V 

A                     H                 "~B 

FIG.  79. 


If  this  mass  of  masonry,  or  other  material,  supports  two 
successive  arches  it  is  called  a  pier;  if  the  pier  be  strong 
enough  to  withstand  the  thrust  arising  from  either  of  the 
arches  alone,  it  is  called  an  abutment  pier;  the  extreme 


ARCHES.  201 

piers  which  support  an  embankment,  generally  of  earth,  on 
one  side,  and  an  arch  on  the  other,  are  called  abutments. 

The  inner  surface  of  the  arch  is  called  the  soffit ;  its  outer 
surface,  the  back.  The  sides  of  the  arch  are  called  reins ; 
the  end  surface,  the  face,  and  sometimes  the  head  of  the 
arch.  The  connection  of  the  arch  with  the  pier  is  called  the 
impost ;  if  the  top  surface  of  a  pier  is  sloped  to  receive  the 
end  of  the  arch,  this  surface  is  called  a  skewback. 

The  highest  stones  of  a  pier,  or  the  stones  on  which  an 
arch  rests,  are  called  cushion  stones  ;  the  highest  stone  of 
the  arch  is  called  the  keystone. 

The  line  in  which  the  soffit  of  the  arch  intersects  the  pier 
is  called  the  springing  line.  The  line  of  intersection  of 
the  face  of  the  arch  with  the  soffit  is  the  intrados ;  with 
the  back  of  the  arch,  the  extrados.  The  chord,  A  B  (Fig. 
79)  is  termed  the  span,  and  the  height,  H  C,  of  the  key- 
stone above  this  line,  is  termed  the  rise.  The  length  of 
the  arch  is  that  of  the  springing  line.  The  highest  line  of 
the  soffit,  that  projected  at  C,  is  called  the  crown.  The 
line  in  the  plane  of  the  springing  lines  projected  at  H,  sym- 
metrically disposed  with  respect  to  the  plan  of  the  soffit  on 
that  plane,  is  the  axis  of  the  arch.  The  courses  of  stones 
parallel  to  the  head  of  the  arch  are  called  ring-courses. 
The  courses  which  run  lengthwise  of  the  arch  are  termed 
string-courses.  The  joints  between  the  different  ring- 
courses  are  called  heading  joints.  Those  between  the 
different  string-courses  are  termed  coursing  orbed-joints. 

A  wall  standing  on  an  arch  and  parallel  to  the  head  is 
called  a  spandrel- wall. 

271.  Classification. — Arches  may  be  classified  according 
to  the  direction  of  the  axis  with  respect  to  a  vertical  or  hori- 
zontal plane,  or  according  to  the  form  of  the  soffit. 

A  right  arch  is  one  whose  axis  is  perpendicular  to  the 
heads.  The  arch  is  called  oblique  or  askew,  when  the  axis 
is  oblique  to  the  heads;  and  rampant,  when  the  axis  is 
oblique  to  the  horizontal  plane. 

Arches  are  termed  cylindrical,  conical,  warped,  etc.,  ac- 
cording as  the  soffit  is  cylindrical,  conical,  etc. 

272.  The  cylindrical  arch. — The  cylindrical  is  the  most 
usual  and  the  simplest  form  of  the  arch.     A  section  taken  at 
right  angles  to  the  axis  is  called  a  right  section. 

These  arches  are  classified  according  to  the  shape  of  the 
curve  cut  out  of  the  soffit  by  the  plane  of  right  section. 

If  the  curve  be  a  semicircle,  the  arch  is  called  a  full 
centre  arch ;  if  a  portion  of  a  semicircle,  a  segmental  arch. 


202 


CIVIL   ENGINEERING. 


When  the  section  gives  a  semi -ellipse,  the  arch  is  called  an 
elliptical  arch ;  if  the  curve  resembles  a  semi-ellipse,  but  is 
composed  of  arcs  of  circles  tangent  to  each  other,  the  term 
oval  of  three,  five,  etc.,  centres,  according  to  the  number  of 
arcs  used,  is  applied  to  designate  it. 

273.  Groined  and  Cloistered  Arches.— The  intersection 
of  cylindrical  arches  having  their  axes  in  the  same  plane,  and 
having  the  same  rise,  form  the  arches  known  as  groined  and 
cloistered. 

The  groined  arch  (Fig.  80)  is  made  by  removing  from 
each  cylindrical  arch  those  portions  of  itself  which  lie  with- 
in the  corresponding  parts  of  the  other  arch ;  in  this  way, 
the  two  soffits  are  so  connected  that  the  two  arches  open 
freely  into  each  other. 


r. 


•  n 


V 

M|         N, 

V— 1 


B\ 


\m 


/B 


FIG."  80 — Represents  the  plan  of  the  soffit  and  the  right  sections  M  and 

N  of  the  cylinders  forming  a  groined  arch. 
aa,  pillars  supporting  the  arch, 
fo,  groins  of  the  soffit. 
om,  mn,  edges  of  coursing  joint. 

A,  key- stone  of  the  two  arches  formed  of  one  block. 

B,  B,  groin  stones,  each  of  one  piece,  situated  below  the  key-stone,  and 
forming  a  part  of  each  arch. 


The  curves  of  intersection  of  the  soffits  form  the  edges  of 
salient  angles  and  are  termed  groins,  hence  the  name  of  the 
arch. 

The  cloistered  arch  (Fig.  81)  is  made  by  retaining  in  each 
cylindrical  arch  only  those  portions  of  itself  which  lie  within 
the  corresponding  portions  of  the  other  arch  ;  thus,  a  portion 


ARCHES. 


203 


of  the  soffit  of  each  arch  is  enclosed  within  the  other,  these 
portions  forming  a  fonr-sided  vaulted  ceiling. 


FIG.  81 — Represents  a  horizontal  section 
through  the  walls  supporting  the  arch  and 
plan  of  the  soffit  of  a  cloistered  arch. 

B,  B,  the  walls  of  the  enclosure  or  abut- 
ments of  the  arches. 

ab,  curves  of  intersection  of  the  soffits. 

«,  e,  groin  stones. 


This  arch  was  much  used  in  forming  the  ceilings  of  the 
cells  of  monasteries ;  from  their  object  and  use  is  derived  the 
term  cloistered. 

274.  Annular  arches. — An  annular  arch  is  one  that  may 
be  generated  by  revolving  the  right  section  of  an  arch  about 
a  line  lying  in  the  plane  of  the  section,  but  not  intersect- 


FiQ.  82. — N,  right  section  of  an  annular  arch. 
C,  plan  of  soffit. 


ing  it     This  line  is  usually  vertical  and  also  perpendicular 
to  the  span  of  the  arch.     (Fig.  £2.)     The  axis  is  curved 


204 


CIVIL   ENGINEERING. 


being  described  by  the  centre  of  the  curve  of  right  section. 
The  coursing  joints  are  conical,  and  the  heading  joints  are 
plane  surfaces. 

275.  Domes. — An  arch  whose  soffit  is  the  surface  of  a 
hemisphere,  the  half  of  a  spheroid,  or  other  similar  surface, 
is  called  a  dome.  The  soffit  may  be  generated  by  revolving 
the  curve  of  right  section  about  the  rise  for  360°,  or  about 
the  span  for  180°.  In  the  first  case  the  horizontal  section  at 
the  springing  lines  is  a  circle,  in  the  other  it  is  the  generating 
curve. 

The  plan  may  be  any  regular  figure.  Fig.  83  represents  a 
plan  and  vertical  section  of  a  circular  dome. 


FIG.  83. — A,  vertical  section  and  elevation  of  a  circular  dome. 
B,  B,  horizontal  section  and  plan  of  its  soffit. 

276.  Conical    arches. — Their  name    explains  their  con- 
struction.    They  are  but  rarely  used,  in  consequence  of  the 
varying  sizes  of  the  voussoirs. 

277.  Arches    with    warped    soffits.  —  Arches,    whose 
soffits  are  warped  surfaces,  are  frequently  used.     The  partic- 
ular kind  of  warped  surface  will  depend*  upon  circumstances. 

A  common  example  of  this  class  is  an  arch  which  has  the 
same  rise  at  the  heads  but  unequal  spans.  The  soffit  in  this 
case  may  be  generated  by  moving  a  straight  line  so  as  to  con- 
tinually touch  the  curves  of  section  of  the  soffit  at  the  heads, 
and  at  the  same  time  to  remain  parallel  to  the  plane  of  the 
springing  lines.  A  surface  generated  in  this  manner  belongs 
to  the  class  of  warped  surfaces  having  a  plane  director.  In 
particular  cases  it  is  a  conoid,  hence  the  name  of  conoidal 
arches  is  frequently  applied  to  this  kind. 


DISTRIBUTION   OF   PBE88UBBL 


205 


Arches  whose  soffits  may  be  thus  generated  possess  the 
advantage  of  having  straight  lines  for  the  edges  or  the  joints 
running  lengthwise  in  the  soffit. 

278.  Oblique  or  askew  arches — An  arch  whose  axis 
makes  an  angle  with  the  head  is  called  oblique  or  askew. 
In  arches  of  this  kind  the  chord  of  the  arc  of  the  head  is  the 
span.  The  angle  of  obliquity  is  the  angle  which  the  axis 
makes  with  a  normal  to  the  head. 


MECHANICS  OF  MASONRY. 

DISTRIBUTION  OF  PRESSURE. 

279.  The  surface  on  which  a  structure  rests  is  required  to 
support  the  weight  of  the  structure,  and  also  the  load  it 
carries,  or  the  thrust  it  may  have  to  resist.     It  is  necessary 
for  stability  that  the  resultant  line  of  these  pressures  should 
pierce  this  surface  within  the  limits  of  the  base  of  the  struct- 
ure, and  that  all  the  forces  acting  within  this  area  be  com- 
pressive.     The  point  in   which  this  resultant  pierces  the 
surface  is  known  as  the  centre  of  pressure. 

Structures  generally  rest  upon  plane  surfaces  .and  the 
portion  pressed  is  usually  a  simple  plane  figure.  Since  the 
pressure  on  this  surface  may  vary  from  point  to  point,  it  is 
necessary  to  determine  what  the  pressure  is  at  any  point  of 
the  surface,  and  to  find  the  limits  within  which  the  centre 
of  pressure  must  be  to  have  all  the  forces  acting  upon  the 
surface  compressive. 

280.  Normal  pressure. — Suppose  a  series  of  blocks,  of 
the  form  of  rectangular  parallelopipedons  with  equal  bases, 
but  (Fig.  84)  whose  altitudes  in- 
crease in  arithmetical   progres- 
sion, be  placed  side  by  side  on  a 

given  plane  area,  A  B  C  D.  It  is 
evident  that  the  pressure  on  the 
area  A  B  C  D,  is  less  on  that  part 
under  block  1  than  it  is  on  the 
part  under  block  5,  and  that  the 
pressure  on  any  part,  as  B  C  5, 
will  be  directly  proportional  to 
the  altitude  of  the  block  resting 
upon  it 

If  these  blocks  be  very  thin, 
that  is,  the  width  of  the  bases 
measured  in  the  direction  of 


FIG.  84. 


A    B    be  infinitely   small, 
and  have  altitudes  that  reach  to  the  line  E  F  drawn  through 


206 


CIVIL    ENGINEERING. 


the  middle  points  of  the  upper  sides  of  blocks  1,  2,  3,  4  and 
5,  the  total  pressure  on  the  area  A  B  C  D  will  be  the  same  as 
that  produced  by  the  five  blocks.  The  pressure  on  the 
units  of  this  area  will  not,  however,  be  the  same,  being  dif- 
ferent for  the  two  cases  for  most  of  them. 

The  pressure  on  each  line  of  the  surface  parallel  to  B  C, 
caused  by  the  thin  blocks,  is  directly  proportional  to  the 
corresponding  ordinate  of  the  trapezoid  B  F  E  A,  and  the 
centre  of  pressure  of  each  block  will  be  found  on  the  sur- 
face A  B  C  D  directly  under  the  centre  of  gravity  of  the 
block.  The  centre  of  pressure  of  the  entire  mass  will  be 
found  on  the  surface  directly  under  the  centre  of  gravity  of  the 
trapezoid  forming  the  middle  section  of  the  thin  blocks. 

281.  Uniform  pressure. — If  the  blocks  were  all  of  the 
same  size  and  of  the  same  material,  the  pressure  on  a  unit  of 


PIG.  85. 


FIG.  86. 


area  would  be  the  same  for  every  point  pressed  by  it,  and  the 
centre  of  pressure  would  be  directly  under  the  centre  of  the 
base.  Assuming  the  form  of  the  base  of  a  structure  to  be 
rectangular,  the  system  of  forces  acting  to  produce  a  press- 
ure that  is  uniformly  distributed  over  the  surface  pressed 
may  be  represented  by  a  rectangular  parallelopipedon  of 
homogeneous  density,  of  which  the  rectangle  is  the  base. 

Suppose  a  rectangular  surface,  as  A  B  C  D  (Fig.  85),  to  be 
pressed  by  such  a  system  of  forces,  and  P  to  be  the  resultant. 


NORMAL    PRESSURE. 


207 


The  centre  of  pressure  would  be  at  the  centre,  0,  of  the 

p 
rectangle,  and  the  pressure  on  each  unit  of  area  would  be  T. 

A 

282.  Uniformly  varying  pressure.  — Suppose  the 
pressure  to  be  zero  along  the  line  A  D  (Fig.  84),  and  to  in- 
crease uniformly  toward  B  C,  along  which  the  pressure  is 
equal  to  B  F.  The  system  of  forces  producing  this  pressure 
may  be  represented  by  a  wedge-shaped  mass  of  homogeneous 
density,  as  shown  in  Fig.  86.  The  centre  of  pressure  of  any 
section  parallel  to  A  B,  is  below  its  centre  of  gravity  and  to 
the  right  of  the  middle  point  of  its  base  at  a  distance  equal  to 
one-sixth  of  A  B.  The  centre  of  pressure  of  the  whole  mass 
will  therefore  be  on  the  line  X  X',  and  at  a  distance  from 
0  equal  to  one-sixth  of  A  B. 

The  pressures  on  the  different  lines  parallel  to  A  D  vary  as 

the  ordinates  of  the  triangle,  N  L  M.     The  pressure  on  the 

p 

unit  at  0,  the  centre  of  the  rectangle,  is  equal  to  -r ,  the  mean 

-A. 

pressure  on  the  surface  of  the  rectangle,  P  being  -the  result- 
ant force. 

To  find  the  pressure  F'  on  the  unit,  at  the  distance  x 
from  0  measured  on  XX',  we  have,  representing  the  sides  of 
the  rectangle  by  2<z  and  2J, 


F'  :  :  N  H  :  N  P,  or  a  :  a  +  x, 


whence,  .  F'  =  ?Y-  +  l) 

jcx  \C6  / 

283.  Uniformly  varying 
pressure  combined  with 
uniform  pressure. — If  we 

suppose  the  wedge-shaped  mass 
of  the  last  case  placed  upon  the 
rectangular  parallelopipedon  of 
the  previous  case,  so  that  the  base 
of  the  wedge  shall  exactly  coincide 
with  the  upper  base  of  the  paral- 
lelopipedon, the  corresponding 
pressure  upon  the  base  may  be 
represented  by  Fig.  87.  In  this 
case,  the  centre  of  pressure  will 
be,  as  before,  below  the  centre 
of  gravity  of  the  mass  represent- 
ing the  system  of  forces  and  to  the 
right  of  the  centre  of  base,  0,  a 


(132) 


FIG. 


208  CIVIL    ENGINEERING. 

distance  less  than  one-sixth  of  A  B.  Represent  the  resultant 
pressure  by  P,  the  distance  0  V  by  as',  and  divide  the  middle 
line  X  X'  into  three  equal  parts,  and  let  K  and  K'  be  the  points 
of  division.  Resolve  the  resultant  P  into  two  parallel  com- 
ponents PI  and  P2,  acting  at  the  points  K  and  K'. 

If  PI  acted  alone,  from  what  we  have  shown,  we  find  the 
pressure  upon  any  unit  due  to  its  action  to  be 

*•- 3(7*'). 

in  which  P'  is  the  pressure  due  to  Pt ;  in  the  same  way  the 
pressure  P"  due  to  P2  acting  alone  would  be 

P»  =  !W_f  +  1)  =  _5(^_A 

A  \     a         I  A\a          f 

The  pressure  P^  due  to  P  will  be  equal  to  their  sum,  or 


To  find  the  value  of  Pt  and  P2  in  terms  of  P,  represent 
these  parallel  components  as  acting  at  M  and  M'.  From  the 
principle  of  parallel  forces,  we  have 

v 

and 


From  which,  finding  the  value  of  Piand  P2,  and  substitut- 
ing in  the  expression  Jor  P^,  we  have 


for  the  pressure  on  the  unit  of  area  at  the  distance  x  from  the 
centre  of  the  base  measured  on  the  line  X  X'. 

284.  Suppose  the  load,  instead  of  being  uniform  along 
lines  parallel  to  X  X',  was  uniform  along  lines  parallel  to  some 
line  making  an  angle  with  it.  If  we  know  the  centre  of 
pressure,  the  pressure  on  any  unit  of  area  of  the  base  may  be 
determined. 

Let  the  centre  of  pressure  be  at  any  point,  as  V  in  the 
rectangle,  and  let  the  co-ordinates  of  this  point  be  denoted  by 
x'  and  y  (Fig.  88). 


NORMAL   PRESSURE. 


Through  V  draw  a  straight  line  Vt  V2,  so  that  v*  shall  be  its 
middle  point.  The  point  v\  would  have  for  its  abscissa  2<r', 
and  V8  for  its  ordinate  2y'. 


The  resultant  P  being  resolved  into  two  parallel  compo- 
nents acting  at  Vt  and  V2,  these  will  be  each  equal  to  -~-. 

From  the  preceding  we  have  the  pressure  at  any  point  pro- 
duced by  a  force  at  Vt  to  be 


3  x  2*aA 
"^       /> 

and  for  that  produced  by  the  force  at  V2  to  be 


2A 


and  hence  the  total  pressure  on  the  unit  of  area  due  to  P 
acting  at  V,  at  the  point  whose  co-ordinates  are  x  and  y,  will 
be 

P/        Sx'x 


The  pressure  at  the  different  points  of  the  base  may  be 
determined  in  a  similar  way  when  the  base  is  a  circle,  ellipse, 
lozenge,  etc. 

285.  General  solution. — It  is  evident  that  there  is  a  ten- 
dency to  produce  rotation  about  some  right  line  in  the  base 
whenever  the  resultant  pressure  pierces  the  plane  of  the 
base  in  any  point  excepting  its  centre  of  figure.  Kegarding 
the  base  as  a  cross-section,  this  right  line  will  be  its  neutral 
axis. 

14 


210  CIVIL   ENGINEERING. 

And  since  the  condition  is  imposed  that  all  the  forces 
acting  within  the  base  shall  be  compressive,  it  is  evident  that 
tliis  neutral  axis  must  remain  outside  of,  or  at  least  tangent  to, 
the  base.  If  the  neutral  axis  should  intersect  the  base,  it  is 
plain  that  the  portion  of  the  base  on  the  same  side  with  the 
centre  of  pressure  would  be  compressed,  while  the  portion  of 
the  base  on  the  other  side  would  be  subjected  to  a  strain  of 
extension,  a  condition  which  is  not  allowable. 

The  centre  of  pressure  of  any  section  is  the  centre  of  per- 
cussion of  the  plane  area  representing  it.  Hence,  the  general 
solution  obtained  from  mechanics  for  obtaining  the  centres  of 
percussion  and  axes  of  rotation  for  any  plane  figure  may  be 
applied  to  these  cases. 

The  normal  pressure  upon  the  base  is  generally  produced 
by  a  uniformly  distributed  load,  by  a  uniformly  varying  one, 
or  by  a  combination  of  the  two,  placed  upon  the  structure. 
These  are  the  cases  which  have  been  considered. 

286.  Symmetrical  base. — In  general  the  blocks  used  in 
building  have  a  plane  of  symmetry,  and  these  loads  above 
named  are  symmetrically  distributed  with  respect  to  this 
plane  and  to  the  base  of  the  block.  It  follows,  therefore, 
that  the  resultant  pressure  pierces  the  base  in  its  axis  or 
middle  line. 

For  such  cases  the  expression  for  the  pressure  on  any  point 
will  be  of  the  general  form, 


in  which  K  is  a  positive  coefficient  depending  upon  the  figure 
of  the  base.  We  have  found  it  equal  to  3  for  the  rectangle ; 
we  would  find  it  equal  to  4  for  the  ellipse  or  circle,  and  6  for 
the  lozenge.  20  being  the  longest  diameter.  Hence  we  con- 
clude that  the  pressure  is  more  equally  distributed  over  a  rect- 
angular base  than  over  a  circular,  elliptical,  or  lozenge-shaped 
one. 

In  the  general  expression  for  Px  it  is  seen  that  in  the 
rectangle  if  x'  is  greater  numerically  than  ±  J#,  that  the 
corresponding  values  of  x  =  =£  #  give  negative  values  for  P,.. 
That  is,  there  will  be  no  pressure  on  the  opposite  edge ;  on 
the  contrary,  there  will  be  tension,  and  the  joint  will  open  or 
tend  to  open,  along  this  line.  If  x'  =  ±  %a  the  values  of  P,, 
for  x  =  ±  a  are  0 ;  that  is.  there  is  no  pressure  on  the  edge. 
Hence,  if  the  pressure  is  to  be  distributed  over  the  entire 
base,  the  resultant  must  pierce  it  within  the  limits  of  ±  %a. 

287.  Oblique   pressure. — In    a  large   number  of    cases, 


STRAINS   ON  MASONRY.  211 

especially  in  structures  of  the  third  and  fifth  classes,  tho 
resultant  pressure  has  its  direction  oblique  to  the  plane  of 
the  base. 

This  resultant  may  be  resolved  at  the  centre  of  pressure 
into  two  components,  one  normal  to  the  plane  of  the  base 
and  the  other  parallel  to  it.  The  former  is  the  amount  of 
force  producing  pressure  on  the  base,  and  is  to  be  considered 
as  in  the  preceding  cases.  The  latter  does  not  produce  pres- 
sure, but  acts  to  slide  the  base  along  in  a  direction  parallel  to 
its  plane.  The  effect  of  sliding  will  be  alluded  to  in  future 
articles. 


MASONRY   STRUCTURES  OP  THE   FIRST  AND   SECOND 
CLASSES. 

288.  The  strains  which  these  structures  sustain  are  pro- 
duced by  vertical  forces. 

For  stability,  the  resultant  pressure  should  pierce  the  plane 
of  the  base  at  a  distance  from  its  middle  line  not  greater  than 
one-sixth  the  thickness  of  the  wall  at  its  base. 

The  wall  having  to  support  a  load,  either  its  own  weight 
alone,  or  its  weight  with  a  load  placed  upon  it,  the  largest 
stones  should  be  placed  in  the  lower  courses,  and  all  the 
courses  so  arranged  that  they  shall  be  perpendicular,  or  as 
nearly  so  as  practicable,  to  the  vertical  forces  acting  on  the 
wall.  Great  care  should  be  taken  to  avoid  the  use  of  con- 
tinuous vertical  joints. 

The  thickness  of  the  wall  will  depend  upon  the  load  it  has 
to  support  and  the  manner  of  its  construction. 


STRUCTURES  OF  THE  THIRD  CLASS. 

289.  Retaining  walls,  besides  supporting  their  own 
weight,  are  required  to  resist  a  lateral  thrust  which  tends  to 
turn  them  over. 

Observation  has  shown  that  if  we  were  to  remove  a  wall 
or  other  obstacle  supporting  a  mass  of  earth  against  any  one 
of  its  faces,  a  portion  of  the  embankment  would  tumble  aown, 
separating  from  the  rest  along  a  surface  as  B  R  (Fig.  89), 
which  may  be  considered  a  plane ;  and  that  later  more  and 
more  of  the  earth  would  fall,  until  finally  a  permanent  slope 
as  B  S  is  reached. 

The  line  B  R,  is  called  the  line  of  rupture,  the  line  B  S 


CIVIL   ENGINEERING. 


the  natural  slope,  and  the  angle  made  by  the  natural  slope 
with  the  horizontal  is  termed  the  angle  of  repose.  The 
angle  C  B  R  is  called  the  angle  of  rupture.  If  dry  sand  be 
poured  out  of  a  vessel  with  a  spout  upon  a  flat  surface,  the 
sand  will  form  a  conical  heap,  the  sides  of  which  will  make 


FIG.  89. 

a  particular  angle  with  the  horizontal,  and  it  will  be  found 
that  the  steepness  of  this  slope  cannot  be  increased,  however 
judiciously  the  sand  may  be  poured,  or  however  carefully  it 
is  heaped  up.  This  slope  or  angle  of  repose  varies  for  differ- 
ent earths,  being  as  much  as  55°  for  heavy,  clayey  earth,  and 
as  little  as  20°  for  fine  dry  sand. 

This  prism  of  earth  C  B  R,  which  would  tumble  down  if 
not  sustained,  presses  against  the  wall,  producing  a  horizontal 
thrust,  and  the  wall  should  be  made  strong  enough  to  resist 
it. 

290.  Two  distinct  problems  are  presented  :  the  first  being 
to  ascertain  the  intensity  of  the  thrust  exerted  against  the  wall 
by  the  earth  ;  and  the  second,  to  determine  the  dimensions 
of  a  wall  of  given  form  so  as  to  successfully  resist  this  thrust. 

The  intensity  of  the  thrust  depends  upon  the  height  of  the 
prism,  and  upon  the  angle  of  rupture. 

The  angle  of  rupture,  or  the  tendency  in  the  earth  to  slip, 
is  not  only  different  for  the  various  kinds  of  earth,  but  is 
different  in  the  same  earth,  according  as  it  is  dry  or  saturated 
with  water,  being  greater  in  the  latter  case. 

The  manner  in  which  the  earth  \&  fitted  i/n,  behind  the  wall, 
affects  the  intensity  of  the  thrust,  the  latter  being  less  when 
the  earth  is  well  rammed  in  layers  inclining  from  the  wall 
than  when  the  layers  slope  towards  it. 

Therefore,  in  calculating  the  amount  of  resistance  the  wall 
should  have,  the  effect  produced  by  the  maximum  prism  of 
pressure  under  the  most  unfavorable  circumstances  should  be 


RETAINING   WALLS.  213 

considered.  The  greatest  pressure  that  earth  can  pi-educe 
against  the  back  or  the  wall  is  when  the  friction  between  its 
grains  are  destroyed,  or  when  the  earth  assumes  the  form  of 
mud.  The  pressure  under  these  circumstances  would  be  the 
same  as  that  produced  by  a  fluid  whose  specific  gravity  was 
the  same  as  earth. 

291.  Retaining  walls  may  yield  by  sliding  along  the  base 
or  one  of  the  horizontal  joints ;  by  bulging ;  or  by  rotation 
around  the  exterior  edge  of  one  of  the  horizontal  joints. 

If  the  wall  be  well  built  and  strong  enough  to  prevent  its 
being  overturned,  it  will  be  strong  enough  to  resist  yielding 
by  the  other  modes. 

Hence,  the  formulas  used  in  determining  the  thickness  of  a 
retaining  wall  are  deduced  under  the  supposition  that  the  only 
danger  to  be  feai^d  is  that  of  being  overturned. 

Having  determined  the  horizontal  thrust  of  the  prism  of 
pressure,  its  moment  in  reference  to  any  assumed  axis  can  be 
obtained. 

A  wall  to  be  stable  must  have  the  moment  of  its  weight 
about  the  axis  of  rotation  greater  than  the  moment  of  the 
overturning  force  about  the  same  line. 

The  term  stability  in  this  subject  differs  slightly  in  its 
meaning  from  that  previously  given  it.  A  mass  is  here  said 
to  be  stable  when  it  resists  without  sensible  change  of  form 
the  action  of  the  external  forces  to  which  it  is  exposed — the 
variations  produced  by  these  forces  being  in  the  reactions  of 
the  points  of  support  and  the  molecular  forces  of  the  body, 
and  not  changing  in  any  way  the  form  of  the  mass. 

The  excess  of  moment  in  the  wall,  or  factor  of  safety,  as 
we  have  heretofore  designated  it,  will  vary  in  almost  every 
special  case,  being  much  greater  for  a  wall  exposed  to  shocks 
than  when  it  has  to  sustain  a  quiescent  mass ;  greater  for  a 
wall  poorly  built,  or  of  indifferent  materials,  than  one  of  bet- 
ter material  and  well  constructed.  The  formulas  which  are 
used  give  results  which  make  this  factor  of  safety  at  least 
equal  to  2,  or  twice  as  strong  as  strict  equilibrium  requires. 


RETAINING  WALLS,  with  back  parallel  to  the  face. 

292.  Let  it  be  required,  to  find  the  thickness  of  a  retaining 
wall,  the  upper  surface  of  the  embankment  being  horizontal 
and  on  a  level  with  the  top  of  the  wall.  The  wall  being  of 
uniform  thickness,  with  vertical  face  and  back. 


CIVIL   ENGINEERING. 


w 

w', 

a, 


Denote  by  (Fig.  90), 

H,  the  height  B  C  of  the  wall, 
5.     "     thickness  A  B  of  the  wall, 

weight  of  a  unit  of  volume  of  the  earth, 

"        "  same  unit  of  volume  of  masonry, 
angle  C  B  S  of  the  natural  slope  with  the  vertl 

cal  B  C, 
fi,  "    angle  S  B  F  of  the  natural  slope  with  the  hori 

zontal. 

Let  it  be  assumed  that  the  density  and  cohesion  of  the 
earth  are  uniform  throughout  the  mass.  The  pressure  ex- 
erted against  the  wall  may  then  be  represented  by  a  single 


FIG.  90. 

resultant  force  acting  through  the  centre  of  pressure  on  the 
surface  of  the  wall. 

If  we  suppose  the  prism  C  B  S  to  act  as  a  solid  piece,  the 
friction  along  B  S  would  be  just  sufficient  to  prevent  sliding, 
and  there  would  be  no  horizontal  thrust.  This  is  true  for 
any  prism  making  an  angle  less  than  /3. 

The  horizontal  thrust  upon  the  back  of  the  wall  must  there- 
fore be  due  to  a  mass  of  earth,  the  lower  surface  of  which 
makes  a  greater  angle  with  the  horizontal  than  ft. 

Let  B  R  be  a  plane  which  makes  an  angle  greater  than  /3, 
and  represent  by  <£  the  angle  which  it  makes  with  the  natural 
slope. 

We  may  suppose  two  cases :  one  in  which  there  is  no  f ric 
tion  existing  between  the  prism  and  the  plane  which  supports 
it ;  and  the  other,  in  which  there  is  friction. 

In  the  first  case,  the  horizontal  thrust  would  be  equal  to 
that  of  a  fluid  whose  specific  gravity  is  the  same  aa  that  of 
the  earth,  or 

Hor.  thrust  = 


the  centre  of  pressure  being  f  H  below  C. 


RETAINING   WALLS.  215 

In  the  second  case,  the  friction  between  the  plane  and 
prism  is  considered,  and  if  we  denote  by  P  the  horizontal 
component  of  the  pressure  acting  to  overthrow  the  wall,  and 
neglect  the  adhesion  and  friction  of  the  earth  on  the  back  of 
the  wall,  we  have,  supposing  <j>  =  \a, 

P  =  -^H2tan8<£      .    .    .    (137) 

The  moment  of  this  force  about  the  edge  A  will  be 

/ 

M  =  froW  tan2  <£  x^H. 


The  moment  of  the  weight  of  the  wall  about  the  «jame  line 
is  M  =  i^I 

a 

Equating  these  moments,  we  have 
whence, 


x 
'   o 


,    ....      (138) 

for  the  value  of  the  thickness  of  base  to  give  the  wall  to  resist 
the  pressure  due  to  P. 

It  can  be  shown  that  the  maximum  prism  of  pressure  will 
be  obtained  when  the  angle  of  rupture,  C  B  R,  is  equal  to 
\  (90°  —  #),  or  equal  to  \a.  This  has  also  been  proved  by  ex- 
periment. Substituting  for  <£  this  value  in  the  expression 
for  J,  and  we  get, 


*aH.tanjy.|.jp 

The  value  for  P  may  be  put  under  the  form, 

o  x  !"Sj"^  (HO) 


which  is  the  form  in  which  it  frequently  appears  in  other 
works  when  treating  this  subject. 
Suppose  B  R  to  coincide  with  B  S,  then  ^  =  0,  and  hence 

P  =  0, 

a  conclusion  already  reached. 


216 


CIVIL   ENGINEERING. 


293.  General  case. — The  wall  was  assumed  vertical  in 
the  preceding  case.  The  general  case  would  be  where  the 

back  of  the  wall  and  the  up- 
J£..- —  per  surface  of  the  embank- 
ment were  both  inclined  to 
the  horizontal.  Let  B  C  (Fig. 
91)  be  the  back  of  the  wall ; 
C  S,  the  upper  surface  of  the 
embankment ;  B  S,  the  line 
of  natural  slope ;  and  <£  and 
ft  represent  the  same  angles 
FIG.  91.  as  in  preceding  example.  The 

pressure  on  the  back  of  the 

wall  is  produced  by  some  prism  as  C  B  R.  The  horizontal 
thrust  produced  by  this  prism  is  equal  to  its  weight  multiplied 
by  the  tan  <£,  or 

P  =  w  x  area  C  B  R  X  tan  <f>. 

Let  it  be  required  to  find  the  maximum  prism  of  pressure. 
This  will  be  a  maximum  when  the  product  of  the  area  C  B  R 
and  the  tan  <f>  is  a  maximum. 

Draw  through  C  and  R  perpendiculars  to  the  line  of  natural 
slope  B  S.  Represent  the  distance  R  L  by  a?,  the  distance  C  K 
by  #,  and  the  distance  B  S  by  b. 

The  area  C  B  R  is  equal  to 


Substituting  in  the  expression  for  P,  we  get 
P  =  w  x  i  b  (a  —  x)  tan  </>. 
Eepresent  the  angle  B  S  C  by  /3',  and  we  can  write 

P  =  w  x  %b(a  —  x)  7  -  —  5j. 
1  b  —  x  cot  ft 

This  expression  is  in  terms  of  a  single  variable  x.     Taking 

ax  -  -  a/2 
the  factor  ^  _  x  c~t"7p?  an(i  differentiating,  and  placing  the 

differential  coefficient  equal  to  zero,  we  get 

(b-x  cot  ft')  (a-2x)-(ax-a?)(-  cot  ft')  =  0, 
whence 

a?cotft'-2bx=  -ab..    .    . 
This  may  be  put  under  the  form 

ab  —  bx  =  bx  —  x2  cot  ft'  =  x(b  —  x  cot  /3'), 
or 

ab  —  bx  —  x  x  B  L. 


RETAINING   WALLS.  217 

Whence, 

area  CBS  —  area  RBS  =  i(a!xBL)  =  area  R  B  L, 
and 

area  R  B  L  =  area  C  B  R, 

or  the  thrust  is  a  maximum  when  the  area  C  B  R  is  equal  to 
the  area  B  R  L. 

If  C  S  is  horizontal  and  B  C  is  vertical,  the  triangle 
R  B  L  is  equal  to  R  B  C  only  when  the  line  B  R  bisects  the 
angle  CBS.  This  result  is  the  same  as  that  of  the  previous 
case. 

Substituting  in  the  expression  for  P,  the  area  R  B  L  for  the 
area  C  B  R,  we  get 

P  =  w  x  area  R  B  L  x  tan  0. 

Substituting  for  this  area  and  for  the  tan  <£,  their  values  in 
terms  of  a?,  we  get 

?  =  %wy?, (142) 

for  the  maximum  thrust. 

From  equation  (141)  we  find  the  value  of  a;  to  be 

x  =  b  tan  ft1  -  Vb  tan  fi'  (b  tan  ft'  -a). 

We  may  write  this  value  x  under  another  form  by  draw- 
ing the  line  B  E  from  B  perpendicular  to  B  S  and  repre- 
senting it  by  c.  We  have  c  =  b  tan  /?',  and  substituting,  we 

get  

x  =  c  —  V  c  (c — a). 
Substituting  this  value  of  x  in  equation  (142),  we  get 

for  the  horizontal  thrust,  produced  by  the  maximum  prism  of 
pressure. 

Knowing  the  horizontal  thrust,  its  moment  around  the 
edge,  A,  can  be  obtained.  The  moment  of  the  wall  around 
the  same  line  is  easily  found. 

Equating  these  moments,  the  value  of  b  can  be  deduced, 
giving  the  requisite  thickness  for  an  equilibrium. 

294.  These  examples  show  the  general  method  used  to  de- 
termine the  thickness  of  retaining  walls. 

The  specific  gravity  of  the  materials  forming  an  embank- 
ment ranges  between  1.4  and  1.9,  and  that  of  masonry  be- 

rt/» 

tween  1.7  and  2.5.  The  ratio  of  the  weights  — ,  is  therefore 
ordinarily  between  £  and  1.  For  common  earth  and  ordinary 


CIVIL  ENGINEERING. 


W 


masonry  it  is  usual  for  discussion  to  assume  — 7  =  |,  and  a  = 

45°.  In  practice  it  is  recommended  to  measure  the  natural 
slope  of  the  earth  to  be  used,  and  to  weigh  carefully  a  given 
portion  of  the  masonry  and  of  earth,  the  latter  being 
thoroughly  moistened. 

In  military  works,  the  upper  surface  of  the  embankment 
is  generally  above  the  top  of  the  wall.  The  portion  of  the 
embankment  above  the  level  of  the  top  is  called  the  surcharge, 
and  in  fortifications  rests  partly  on  the  top  of  the  wall.  "When 
its  height  does  not  exceed  that  of  the  wall,  the  approximate 
thickness  of  the  wall  may  be  obtained  by  substituting,  the 
sum  of  the  heights  of  the  wall  and  the  surcharge,  for  H  in 
the  expression  for  the  thickness  already  obtained. 

The  manner  in  which  earth  acts  against  a  wall  to  overturn 
it  cannot  be  exactly  determined,  hence,  the  thrust  not  being 
exactly  known,  the  results  obtained  are  only  approximations. 
Nevertheless,  a  calculation  right  within  certain  limits  is  better 
than  a  guess,  and  its  use  will  prevent  serious  mistakes  being 
made.  • 


FIG.  92. 

In  our  discussion  the  cohesion  of  the  particles  of  earth  to 
each  other  and  their  friction  on  the  back  of  the  wall  have 
been  disregarded.  The  results  therefore  give  a  greater  thick- 
ness than  is  necessary  for  strict  equilibrium,  and  hence  errs 
on  the  side  of  stability. 

295.  Among  the  many  solutions  of  this  problem,  those  given 


RETAINING  WALLS. 


219 


oy  M.  Poncelet,  and  published  in  No.  13  "  Du  Memorial  de 
POfficier  du  Genie,"  are  the  most  complete  and  satisfactory. 

In  this  memoir  he  gives  a  table  from  which  the  proper 
thickness  of  a  retaining  wall  supporting  a  surcharge  of  earth 
may  be  obtained. 

The  principal  parts  of  this  table  giving  the  thickness  in 
terms  of  the  height,  for  surcharges  whose  heights  vary  be- 
tween 0  and  twice  the  height  of  the  wall,  are  as  follows : 

Kepresent  by  (Fig.  92). 

H,  the  height  B  C  of  the  wall ; 

A,  the  mean  height  of  C  F  of  surcharge ; 

a,  the  angle  CBS  made  by  the  vertical  with  line  of  natu- 
ral slope  B  S. 

/?,  the  angle  of  natural  slope  with  the  horizontal ; 

J9  the  coefficient  of  friction  =  cotan  a  ; 

if,  the  distance  from  foot  of  surcharge  E  to  D  outer  edge 
of  wall ; 

Wj  weight  of  unit  of  volume  of  earth ; 

w\  weight  of  unit  of  volume  of  masonry. 

TABLE. 


1 

RATIO  OP  HEIGHT  TO  THICKNESS,  OB  5 

B 

When  w=-w'  and 

V>  =  §to' 

—  I* 

/=0.6 
0  =  81° 

/=1.4 
0  =  51*  25' 

/=  0.6  0  =  31° 

/=1'4°2y 

W=0 

•=*» 

«=o 

-*» 

«=° 

-*H 

«=° 

-*" 

»=0 

U=iH 

0 

0.452 

0.452 

0.258 

0.258 

0.270 

0.270 

0.350 

0.350 

0.198 

0.198 

0.1 

0.498 

0.507 

0.282 

0.290 

0.303 

0.306 

0.393 

0.393 

0.222 

0.229 

0.2 

0.548 

0.563 

0.309 

0.326 

0.336 

0.342 

0.439 

0.445 

0.249 

0.262 

0.4 

0.665 

0.670 

0.369 

0.394 

0.399 

0.405 

0.532 

0.522 

0.303 

0.299 

0.6 

0.778 

0.754 

0.436 

0.450 

0.477 

0.457 

0.617 

0.572 

0.360 

0.328 

03 

0.867 

0.820 

0.510 

0.501 

0.544 

0.504 

0.668 

0.610 

0.413 

0.357 

1 

0.930 

0.873 

0.571 

0.546 

0.605 

0.540 

0.707 

0.636 

0.457 

0.384 

2 

1.107 

1.004 

0.812 

0.714 

0.795 

0.655 

0.811 

0.705 

0.622 

0.475 

220 


CIVIL   ENGINEERING. 


The  thickness  obtained  by  using  "  this  table  are  nearly 
double  that  of  strict  equilibrium.  This  factor  of  safety  01 
excess  of  stability  is  that  used  by  Vauban  in  his  retaining 
walls  which  have  stood  the  test  ol  more  than  a  century  with 
safety. 

The  formula, 


=  0.845  (H  +  h)  A™_  x  tan    ±5°  - 


will  give  very  nearly  the  same  values  as  those  given  in  the 
table. 

RETAINING  WALLS,  face  and  back  not  parallel. 

296.  To  transform  a  wall  of  rectangular  cross-section  into 
one  of  equal  stability  having  a  batter  on  its  face  and  its  back 
vertical,  the  usual  form  of  cross-section  of  a  retaining  wall, 
we  may  use  the  following  formula  of  M.  Poncelet, 


V  =  I  +       n  H. 


(145) 


in  which  (Fig.  93)  b  =  the  thickness,  B  d,  of  wall  of  rectangu- 
lar cross-section, 


FIG.  93. 

V  =  the  base,  A  B,  of  the  equivalent   wall  with  trapezoidal 
cross-section, 

H  =  the  height  B  C  of  the  wall,  and  n  =  the  quotient  ^-f . 

D  r 

The  base  of  the  rectangular  wall  for  the  height,  H,  is  ob- 
tained from  the  previous  formulas,  then,  knowing  n,  the  value 
of  I'  is  obtained  from  formula  (145). 


COUNTERFORTS.  221 

Tiiat  is,  the  thickness  of  the  equivalent  trapezoidal  wall  at 
the  base  is  equal  to  the  thickness  of  the  rectangular  wall  in- 
creased by  one-tenth  of  the  product  obtained  by  multiplying 
the  height  of  the  wall  by  the  quotient  resulting  from  dividing 
the  base  of  the  slope  by  its  perpendicular.  This  rule  gives 
the  thickness  to  within  T£Q-  of  the  true  distance  for  values 
of  n  less  than  •$-,  and  within  ^5-  for  values  less  than  £.  Batters 
with  a  slope  less  than  J  are  seldom  used. 

297.  Counterforts. — Counterforts  are  considered  to  give 
additional  strength  to   a  wall  by  dividing  it   into  shorter 
lengths,  these  short  lengths  being  less  liable  than  longer  ones 
to  yield  by  bulging  out  or  sliding  along  the  horizontal  courses ; 
by  the  pressure  being  received  on  the  back  of  the  counterfort 
instead  of  on  the  corresponding  portion  of  the  wall,  thus 
increasing  the  stability  of  the  wall  against  overturning  at 
those  points ;  and  by  the  filling  being  confined  between  the 
sides  of  the  counterforts,  the  particles  of  the  filling,  especially 
in  case  of  sandy  material  when  confined  laterally,  becoming 
packed  and  thus  relieving  the  back  of  the  wall. 

Counterforts  are,  however,  of  doubtful  efficiency,  as  they 
increase  the  stability  of  the  wall  but  slightly  against  rotation, 
and  not  at  all  against  sliding.  They  certainly  should  not  be 
used  in  treacherous  foundations  on  account  of  the  danger  of 
unequal  settling. 

The  moment  of  stability  of  a  wall  with  counterforts  may 
be  found  with  sufficient  accuracy  for  all  practical  purposes 
by  adding  together  the  moments  of  stability  of  one  or  the 
parts  between  two  counterforts,  and  one  of  the  parts  aug- 
mented by  a  counterfort,  and  dividing  this  sum  by  the  total 
length  of  the  two  parts. 

Their  horizontal  section  may  be  either  rectangular  or 
trapezoidal.  The  rectangular  form  gives  greater  stability 
against  rotation,  and  costs  less  in  construction;  the  trape- 
zoidal form  gives  a  connection  between  the  wall  and  coun- 
terfort broader  and  therefore  firmer  than  the  rectangu- 
lar, a  point  of  some  consideration  where,  from  the  char- 
acter of  the  materials,  the  strength  of  this  connection  must 
mainly  depend  upon  the  strength  of  the  mortar  used  for  the 
masonry. 

298.  Counterforts  have  been  used   by  military  engineers 
chiefly  for  the  retaining  walls  of   fortifications.     In  regu- 
lating their  form  and  dimensions,  the  practice  of  Vauban 
has  been  generally  followed ;  this  is  to  make  the  horizontal 
section  of  the  counterfort  trapezoidal,  to  make  the  length,  ef, 
of  the  counterfort  (Fig.  94)  equal  to  two-tenths  of  the  height 


CIVIL  ENGINEERING. 

of  the  wall  added  to  two  feet,  the  front,  ab,  one-tenth  ofih* 
height  added  to  two  feet,  and  the  back,  cd,  equal  to  two- 
thirds  of  the  front,  ab. 


FIG.  94 — Represents  a  section  A  and  plan  D  of  a 
wall,  and  an  elevation  B  and  plan  E  of  a  trape 
zoidal  counterfort. 


RESERVOIR   WALLS   AND   DAMS. 

299.  These  are  retaining  walls  which  are  used  to  resist  the 
pressure  of  a  volume  of  water  instead  of  earth,  and  they  do  not 
differ  mathematically  from  the  walls  already  discussed.  Their 
dimensions  are  therefore  obtained  in  the  same  way. 

Their  cross-section  is  generally  trapezoidal. 

Let  A  B  C  D  (Fig  95)  represent  the  cross-section  of  a  reser- 
voir wall,  with  a  vertical  water  face  B  C,  and  let  the  upper 
surface  of  the  water  be  at  E  F. 

Represent  by 

A,  the  depth  E  B  of  the  water ; 

h',  the  height  B  C  of  the  wall ; 

5,  b',  the  upper  and  lower  bases  A  B  and  D  C ; 

10,  the  weight  of  unit  of  volume  of  water  ; 

w',  the  weight  of  unit  of  volume  of  masonry. 

Lay  off  B  H  equal  to  one-third  of  B  E,  and  draw  the  nori* 
zontal  H.  This  gives  the  direction  and  point  of  application 
of  the  thrust  on  the  wall  produced  by  the  pressure  of  the 
water.  Its  intensity  is  equal  to  %w/i*.  The  weight  of  the  wall 
acts  through  the  centre  of  gravity  G,  and  is  equal  to  \w'h' 
(b  +  bf).  The  moments  around  the  edge  at  A  can  be  deter- 
mined and  the  values  for  b  and  b'  found. 


RESERVOIR    WALLS. 


223 


The  resultant  E  of  these  pressures  intersects  the  base  A  B 
between  A  and  B.     Stability  requires  that  this  should  be  so. 


FIG.  95. 

If  the  resistance  to  a  crushing  force  were  very  great  in  the 
surface,  A  B,  supporting  the  wall,  it  would  make  no  difference 
how  near  the  resultant  came  to  the  edge  A.  But  r.s  such  is' 
not  the  case,  it  should  not  come  so  near  the  edge  as  to  pro- 
duce a  pressure  along  the  latter  sufficiently  great  to  injure 
the  resistance  of  the  material. 

The  nearer  the  intersection  is  to  the  middle  point  of  the 
base,  the  more  nearly  will  the  pressure  on  the  foundation  of 
the  wall  be  uniformly  distributed  over  it. 

It  is  evident,  from  the  figure,  that  the  batter  given  to  the 
face  A  D  contributes  greatly  to  the  uniform  distribution  of  the 
pressure.  And  it  is  easily  seen  that  if  the  outer  face  had 
been  made  vertical,  the  resultant  would  have  intersected  the 
base  much  nearer  to  the  edge  A,  producing  a  far  greater  pres- 
sure in  that  vicinity  than  in  the  former  case. 


0      C 


FIG.  90. 


300.  Reservoir  walls  are  usually  constructed  with  both  their 
faces  sloped      Having  found  the  thickness  of  the  wall,  as 


224 


CIVIL   ENGINEERING. 


above,  the  profile  is  easily  transformed.  For  example,  let 
A  B  C  D  (Fig.  96)  be  a  cross-section  of  a  wall  in  which  b  and 
bf  have  been  determined  by  previous  rule.  Let  M  N  be  the 
thickness  at  the  middle  point  of  the  inner  vertical  face.  It  is 
evident  that  if  the  thickness  at  top  be,  diminished  by  0  C,  and 
that  at  the  base  be  increased  by  the  equal  quantity  B  P,  that 
the  weight  of  the  wall  will  remain  the  same,  with  an  increase 
of  stability. 

STRUCTURES  OF  THE  FOURTH  CLASS. 

301.  Structures  belonging  to  this  class  sustain  a  transverse 
strain.  Since  stone  resists  poorly  a  cross-strain,  great  caution 
must  be  used  in  proportioning  the  different  parts  of  these 
structures.  The  rules  for  determining  the  strength  of  beams 
subjected  to  transverse  strains  can  be  applied. 


STRUCTURES  OF  THE  FIFTH  CLASS. 

302.  Arches  are  the  principal  structures  belonging  to  this 
class.     They  are  used  to  transmit  the  pressure  they  directly 
receive  to  lateral  points  of  support. 

Arches  are  generally  made  symmetrical,  hence  the  condl- 
tions  of  stability  deduced  for  either  half  are  equally  applica- 
ble to  the  other. 

303.  Modes  of  yielding.— Arches  may  yield  either  by 
sliding  along  one  of  their  joints,  or  by  turning  around  an  edge 
of  a  joint. 


FIG.  97. 


Suppose  the  arch  to  be  divided  into  equal  halves  by  its 
plane, of  symmetry,  and  let  the  right  portion  be  removed 


AECHE8. 


225 


(tig.  97).  "We  may  suppose  the  equilibrium  preserved  by 
substituting  a  horizontal  force  H  for  the  half  arch  removed. 

If  the  semi-arch  were  one  single  piece,  the  intensity  of  this 
force,  H,  could  be  easily  determined,  for  the  conditions  of 
equilibrium  would  require  the  moment  of  the  weight  of  the 
semi-arch  around  the  springing  line  at  A  to  be  just  equal  to 
the  moment  of  H  about  the  same  line. 

The  semi-arch  not  being  a  single  piece,  but  composed  of 
several,  mav  separate  at  any  of  the  joints,  and  therefore  the 
difficulty  of  determining  the  values  of  H  is  increased. 

CONDITIONS  OP  STABILITY  to  prevent  sliding  at  the  joints. 

304.  The  resistance  to  sliding  arises  from  the  friction  of 
the  joints  and  from  their  adherence  to  the  mortar. 

Arches  laid  in  hydraulic  mortar,  or  thin  arches  in  common 
mortar,  may  derive  an  increase  of  stability  from  the  adhesion 
of  the  mortar  to  the  joints,  but  in  our  calculations  we  should 
disregard  this  increase,  and  depend  for  stability  upon  the 
resistance  due  to  friction  alone. 

It  is  found  that  friction,  when  the  pressure  is  constant,  is 


FIG.  98. 


independent  of  the  area  of  the  surfaces  in  contact,  and  de- 
pends solely  upon  the  nature  and  condition  of  the  surfaces. 

Let  F  be  the  resistance  to  sliding,  produced  by  friction  at 
any  joint  I  K  (Fig.  98).     The  external  forces  acting  on  this 
15 


226  CIVIL   ENGINEERING. 

joint  are  the  horizontal  force  H,  and  the  weight  of  the  mass 
K  B  C  I.  Denote  by  R  the  resultant  of  these  forces,  and  con- 
struct it.  This  resultant  pierces  the  plane  of  the  joint  I  K  at 
Borne  point  as  M,  and  M  N  will  be  the  normal  component. 
Represent  by  P  this  normal  component,  and  by  S  the  com- 
ponent parallel  to  the  joint.  We  have 


in  which/*  is  the  coefficient  of  friction  determined  by  experi- 
ment. 

In  order  that  sliding  along  this  joint  shall  not  take  place, 
we  must  have 

S<  F,  orS</P,    whence 


o 

But  pis  equal  to  the  tangent  of  the  angle  which  the  result- 

ant R.  makes  with  the  normal  to  the  joint.  Hence  we  con- 
clude that  when  the  angle  made  by  the  resultant  of  the  pres- 
sures with  the  normal  to  the  surface  of  the  joint  is  less  than 
the  angle  of  friction  of  the  blocks  on  each  other,  that  there 
will  be  no  sliding. 


CONDITIONS  OP  STABILITY  to  prevent  rupture  by  rotation. 

305.  Take  any  joint,  as  I  K  (Fig.  98).  The  arch  may  give 
way  by  opening  at  the  back  and  turning  around  the  lower 
edge  at  K,  or  by  opening  on  the  soffit  and  turning  around  the 
edge  at  I. 

Let  us  suppose  the  first  case,  or  that  the  arch  opens  at  the 
back.  Denote  by  x  the  lever  arm  of  the  weight  W  of  the 
mass  K  B  C  I,  and  by  y  the  lever  arm  of  the  force  H,  both  as 
and  y  being  taken  with  respect  to  the  edge  K. 

For  stability  we  must  have 

H  x  y  -  Wx  >  0. 

Suppose  the  second  case,  or  that  the  arch  opens  at  K,  and 
denote  by  u  and  v  the  lever  arms  of  W  and  H  with  respect 
to  I.  We  must  have  for  stability 


If  we  find  the  joints   at  which  "W  —  is  a  maximum  and 

y 


JOINTS   OF    RUPTURE.  227 

M 

W-  is  a  minimum,  then  for  stability  the  value  of  H  must 

lie  between  these  two  values. 

That  is,  the    condition  for  stability  against  rupture  by 
rotation  around  the  edge  of  a  voussoir  requires  the  thrust,  H  of 

the  arch  to  be  greater  than  the  maximum  value  of  W-,  and 

less  than  the  minimum  value  of  W-. 

J      v 


Joints  of  Rupture. 

306.  From  observations  made  on  the  manner  in  which  large 
arches  have  settled,  and  from  experiments  made  in  rupturing 
small  ones,  it  appears  that  the  ordinary  mode  of  fracture  is 
for  the  arch  to  separate  into  four  pieces,  presenting  five  joints 
of  rupture. 

Cylindrical  arches  in  which  the  rise  is  less  than  half  the 
span,  and  the  full  centre  arch,  yield  by  the  crown  settling  and 
the  sides  spreading  out  The  vertical  joint  at  the  crown 


FIG-  99. 

opens  on  the  soffit,  the  reins  open  on  the  back,  and  if  there 
be  no  pier,  the  joints  at  the  springing  line  open  on  the  soffit 
(Fig.  99). 

The  two  lower  segments  revolve  outwardly  on  the  exterior 
edge  of  the  joints,  leaving  room  for  the  upper  segments  to 
revolve  towards  each  other  on  the  interior  edges  of  the  joints 
at  the  reins. 

This  is  almost  the  only  mode  of  yielding  for  the  common 
cylindrical  arch.  If  the  thickness  be  very  great  compared 
with  the  span,  the  rupture  will  take  place  by  sliding.  As  a 
rule,  this  mode  of  rupture  never  does  take  place  for  the  reason 
that  the  arch  will  rupture  by  rotation  around  a  joint  before 
it  will  yield  by  sliding. 


228  CIVIL   ENGINEERING. 

Yery  light  segmental  arches,  full-centre  aruhes  which  are 
slightly  loaded  at  the  crown  and  overloaded  at  the  reins,  and 
pointed  arches,  are  liable  to  rupture,  as  shown  in  Fig.  100. 

In  this  case  the  crown  rises  and  the  sides  fall  in ;  the  open- 


FIG.  100. 

ing  of  the  joints  and  the  rupture  occur  in  a  manner  exactly 
the  reverse  of  that  just  described.     This  mode  of  rupture  is 
still  more   uncommon  than  that  by  sliding;   for  all  these 
teasons,  the  condition 

H  x  y  —  Wx  >  0 
is  in  general  the  one  applied  to  test  the  stability  of  the  arch. 


Cylindrical  Arch. 

307.  Let  it  be  required  to  find  the  conditions  o'f  equili- 
brium for  a  full  centre  arch. 

The  strains  in  the  arch  are  produced  by  the  weight  of  the 
arch  stones,  the  load  placed  upon  the  arch  and  the  reactions 
at  the  springing  lines. 

The  object  of  this  discussion  is  to  show  how  these  external 
forces  may  be  determined  and  how  to  arrange  the  joints  and 
fix  the  dimensions  of  the  voussoirs  so  as  to  resist  successfully 
the  action  of  these  forces. 

The  joints  are  the  weak  places,  since  the  separation  of  the 
parts  at  these  points  is  not  resisted  by  the  material  of  which 
the  arch  is  made. 

AB  before  stated,  the  arch  may  yield  by  sliding  along  one 
of  the  joints  or  by  turning  around  an  edge.  The  first  mode 
of  yielding  may  be  prevented  by  giving  the  plane  of  the  ioint 
such  a  position,  that  its  normal  shall  make  with  the  resultant 
pressure  an  angle  less  than  the  angle  of  friction  of  the  ma- 
terial of  which  the  voussoirs  are  made. 


CYLINDRICAL   ARCH. 


This  is  usually  effected  by  making  the  coursing  joints  nor- 
mal to  the  ring  courses  and  to  the  soffit  of  the  arch. 

Since  there  is  little  danger  of  the  arch  rupturing  by  the 
crown  rising  and  the  sides  falling  in,  we  make  use  of  the 
formula 

H  x  y-Wx  >  0. 

The  additional  condition  is  imposed  that  the  whole  area  of 
the  joint  must  be  subjected  to  compression.  It  therefore 
follows  that  the  resultant  of  the  external  forces  must  pierce 
the  joint  within  its  middle  third. 

Since  the  form  of  the  arch  is  known,  the  direction  of  the 
coursing  joints  chosen,  and  the  limits  of  the  resultant  deter- 
mined, it  will  only  be  necessary  to  find  where  the  resultant 
pierces  each  joint  and  see  if  the  angle  it  makes  with  the  nor- 
mal is  less  than  the  angle  of  friction,  and  that  the  resultant 
pierces  the  plane  of  the  joint  within  the  required  limits. 

Cylindrical  Arch,  Unloaded. 

308.  For  simplicity,  let  us  consider  the  arch  to  be  a  full 
centre,  the  extrados  and  intrados  being  parallel  and  the 
arch  not  loaded. 


•',-.-••,  •    -.-    /  ,:  's. 


FIG.  101. 


Let  I  K   (Fig.  101)  oe  a  joint  of  the  arch  whose  thicknosi 
in  the  direction  of  the  length  of  the  arch  is  unity. 
Represent  by 

R,  the  radius  of  the  extrados  ; 
r,  the  radius  of  the  intrados  ; 

<£.  the  angle  made  by  the  joint  I  K  with  the  vertical ; 
W  and  H,  same  as  in  previous  case  ; 
g,  the  centre  of  gravity  of  the  ring  K  B  C  I ; 
to,  the  weight  of  a  unit  of  volume  of  masonry 


230  CIVIL   ENGINEERING. 

The  point  of  application  of  the  thrust  H,  at  the  joint  B  C 
is  somewhere  above  the  middle  of  the  joint,  and  when  the 
arch  begins  to  rupture  it  is  at  C  (Fig.  101).  The  condition 
of  stability  for  this  case  at  the  joint  I  K  is 

W-=H. 

y 

If  the  values  of  x  and  y  be  found  in  known  terms,  and  sub- 
stituted in  this  expression,  the  horizontal  thrust  can  be 
determined. 

To  find  these  values  of  x  and  y,  denote  by  u  the  distance 
of  the  centre  of  gravity  g  from  0,  and  by  UL  and  u%  the  dis- 
tances of  the  centres  of  gravity  of  the  sectors  I  0  C  and  K  0  B 
from  the  same  point.  We  have 

M!  x  sector  I  0  C  =  w2  x  sector  K  0  B  +  u  x  ring  K  B  C  I. 

The  areas  of  the  sectors  are  ^R2</>  and  -Jrfy,  hence  the  area 
of  K  B  C  I  is  equal  to  £<£  (E2-/^). 
We  find  (Anal.  Mech.,  par.  121,  p.  96)  the  values  of  11^  and 


3      arc$  3       arc$ 

Substituting  for  the  areas,  and  for  %  and  u%  their  values 
as  above,  and  solving  with  respect  to  u,  we  have 

u  _  4  E3  —  r3    sin^ft 
3K2  —  r*'    arc<£  * 

Now  x  is  equal  to  K  M  —  N\gf  =  r  sin  <£  —  Og  sin  £<£,  whence 


and  y  —  R  —  r  cos  <f>. 

T> 

Hence,  by  writing  k  for  _,  we  have 

T 

H  =  ^.  =  rtw  ism  4>  ffi*—l)  ^Q  ^-—         —  cos 


y  —  cos  <> 

.     .     (146) 

an  expression  for  the  horizontal  thrust,  in  terms  of  R,  r,  w, 
and  <f>,  which  force  applied  to  the  arch  at  C  will  prevent  the 
rotation  of  the  volume  K  C  B  I  around  the  edge  K. 


CTLESDEICAL    ARCH. 


231 


Th:s  expression  might  be  differentiated  with  respect  to  <f>, 
and  that  value  for  <£  obtained,  which  would  make  H  a  maxi- 
mum. This  maximum  value  thus  found,  if  applied  to  the 
arch  at  C,  would  prevent  its  rotation  around  any  edge  on  the 
soffit. 

309.  Instead  of  differentiating  as  suggested,  it  is  usual  in 
practice  to  take  the  above  expression  for  H,  calculate  the 
values  for  every  ten  degrees,  and  select  for  use  the  greatest 
of  these  values.  This  greatest  value  thus  obtained  will  differ 
but  slightly  from  the  true  maximum. 

If  we  assume  k  =  1.2,  r  =  10  feet,  B,  =  12  feet,  and  w  = 
150  pounds,  and  find  the  values  of  H  for  the  different  values 
of  $  for  every  ten  degress  from  10°  to  90° ;  we  may  tabu- 
late them  as  follows : 


Values  of  +. 

Values  of  H  in  pounds. 

10° 

208 

20° 

670 

30° 

1,127 

40° 

1,450 

60° 

1,625 

60° 

1,675 

70° 

1,662 

80° 

1,490 

90° 

1,285 

A  calculation  for  </>  =  57°  gives  H  =  1,672,  63°  gives  1,670, 
and  65°  gives  1,661  pounds. 

The  angle  requiring  the  maximum  thrust  is  very  nearly  60°. 

310.  The  foregoing  applies  only  to  an  unloaded  full  centre 
arch,  its  extrados  and  intrados  being  parallel.  All  arches 
carry  loads  which  frequently  rise  above  the  arch  to  a  surface 
either  horizontal  or  nearly  so.  It  is  evident  that  if  verticals 
be  erected  at  the  joints,  and  be  produced  until  they  meet  the 
upper  surface  of  the  load,  that  they  will  define  and  limit 
the  load  resting  on  each  voussoir.  An  analogous  process  to 
that  just  given  will  enable  the  student  to  determine  the  hori- 
zontal thrust  in  tire  arch  thus  loaded. 


232 


CIVIL   ENGINEERING. 


Prof.  Rankine  gives  the  following  rule  to  find  the  approxi- 
mate horizontal  thrust  in  a  full  centre  arch  loaded  as  shown 
in  the  figure.  (Fig.  102.) 


FIG.  102. 


The  horizontal  thrust  is  nearly  equal  to  the  weight  sup* 
ported  between  the  crown  and  that  part  of  the  soffit  whose 
inclination  is  45°. 

The  approximate  thrust  obtained  by  this  rule  seldom  differs 
from  the  true  horizontal  thrust  by  so  much  as  one-twentieth 
part. 

Represent  by  (Fig.  102). 

R,  the  radius  0  D  of  the  extrados  ; 

7",  the  radius  0  C  of  the  intrados ; 

GJ  the  distance    D  E,  F  E  being  horizontal ; 

w,  the  weight  of  a  cubic  foot  of  masonry  ; 

w',  the  weight  of  a  cubic  foot  of  the  load  resting  on  the 
arch ; 

H,  the  horizontal  thrust  required. 

Draw  0  K  making  an  angle  of  45°  with  the  vertical ;  then, 
the  horizontal  thrust  of  the  arch  on  the  pier  at  A  is  stated  to 
be  nearly  equal  to  the  weight  of  the  mass  C  K  I  F  E,  which 
lies  between  the  joint  I  K  and  the  vertical  plane  through  C  ; 
hence, 

H  =  w'  R  (.0644  R  +  .7071  c)  +  .3927  w  (R2-/-2).    (147) 

for  the  value  of  the  horizontal  thrust. 

The  edge  I  is  at  the  level  to  which  it  is  advisable  to  build 
the  backing  solid,  or  at  least  to  give  the  blocks  a  bond  which 
will  render  the  mass  effective  in  transmitting  the  horizontal 
thrust. 


CURVE   OF   PRESSURE. 


In  the  case  of  a  segmental  arch,  Eankine  takes  the  weight 
of  half  the  arch  with  its  load,  and  multiplies  it  by  the  co- 
tangent of  the  inclination  of  the  intrados,  at  the  springing 
line,  to  the  horizon  ;  the  result  is  the  approximate  value  of  H. 

311.  Having  determined  the  value  for  H  for  the  given 
arch,  combine  it  with  the  external  forces  acting  on  the  first 
voussoir  at  the  crown  and  construct  their  resultant.     The 
point  in  which  this  resultant  pierces  the  joint  will  be  the 
centre  of  pressure  for  that  joint.     Do  the  same  for  the  other 
joints  and  the  intensity  of  the  resultant  and  the  centre  of 
pressure  for  each  joint  are  known. 

If  these  resultants  be  produced,  a  polygon  will  be  formed, 
each  angle  of  which  will  be  on  the  resultant  of  the  external 
forces,  acting  on  the  voussoir  between  the  two  joints  to  which 
the  sides  of  the  polygon  correspond.  A  curve  inscribed  in 
this  polygon  tangent  to  its  sides  is  called  the  curve  of 
pressure  of  the  arch,  since  a  right  line  drawn  through  a 
centre  of  pressure,  tangent  to  this  curve,  will  give  the  direc- 
tion of  the  resultant  pressure  for  this  point. 

If  normals  be  drawn  through  the  centres  of  pressure  a 
polygon  will  be  formed  whose  sides  give  the  direction  of  the 
components  producing  pressure  on  the  joints.  A  durve 
tangent  to  its  sides  is  called  the  curve  of  resistance,  and 
is  the  locus  of  the  centres  of  pressure  of  the  joints. 

For  stability,  the  curve  of  resistance  should  pierce  each 
joint  in  its  middle  third,  and  the  curve  of  pressure  should  be 
so  situated  that  right  lines  tangent  to  it  drawn  through  the 
centres  of  pressure  should  make  angles  with  the  normals  less 
than  the  angle  of  friction. 

312.  Equation  of  the  curve  of  resistance. — Suppose 
the  loads  on  an  arch  to  be  symmetrically  disposed  so  that 
the  resultant  forces  will  lie  in  a  vertical  plane. 

Equations  (688)  of  Anal.  Mechanics  for  this  case  will  be 
*.  o 


(148) 


FIQ.  103. 

in  which  H  is  the  horizontal  thrust  at  0  (Fig.  103)  ;  C  the 
compressive  stress  on  any  section,  ae  D  ;  £,  the  length  of  any 
portion  of  the  curve,  as  6  D ;  and  W  the  sum  of  the  vertical 
forces  acting  on  the  portion  considered. 


234  CIVIL  ENGINEERING. 

The  first  of  equations  (148)  shows  that  the  horizontal  com- 
ponent of  the  force  of  compression  at  any  joint  is  equal  to 
the  horizontal  thrust  at  the  crown,  or  is  the  same  at  every 
section  of  the  arch. 

The  second  of  these  equations  shows  that  the  vertical  com- 
ponent of  the  force  acting  at  any  joint  is  equal  to  the  load 
between  the  vertical  plane  through  the  crown  and  the  section 
considered. 

313.  Suppose  an  arch  loaded  as 
shown  in  figure  (104) ;  the  material 
being  homogeneous  and  the  Veight 
of  a  unit  of  volume  being  represented 
by  w.  Represent  0  F  by  a. 
FIG.  104.  The  weight  of  the  volume  resting 

on  the  arch  between  the  vertical  section  at  D  and  the  consecu- 
tive section  is 

(adx  +  ydx)w. 

Taking  this  between  the  limits,  0  and  a?,   we  get 


( ax  +  J     ydx  W, 


for  the  load  resting  on  0  D.     Substituting  this  in  the  second 
of  equations  (148)  for  W,  we  get 


(ax  +  jf*  yda\  -0^  =  0.    .     (149) 


w  (ax 


Combining  this  equation  with  the  first  of  equations  (148),  we 
have 


whence,  by  differentiating,  we  get 


. 

Integrating  this  differential  equation  twice,  we  gel:  the 
equation  of  the  curve,  and  find  it  to  be  a  transcendental  line. 

314.  If  the  load  had  been  placed  on  the  arch  so  as  to  be  a 
function  of  the  first  power  of  the  abscissa,  that  is,  if  the  load 
between  the  origin  and  any  section  whose  abscissa  is  a,  was 
then  equations  (148)  would  have  taken  the  form 


ds 


CUEVE   OF    RESISTANCE.  235 

Whence,  by  combination, 


and  by  integration, 

y  =  maf-  •  •  •  •    <152) 

which  is  the  equation  of  a  parabola. 

315.  Polar  equation  of  the  curve  of  resistance.— 

This  equation  is  deduced  by  General  Woodbury  as  follows : 

Kepresent  by  (Fig.  105) 

H,the  horizontal  thrust  at  ra;  mnp, 
the  curve  of  resistance  ;  /•',  the  dis- 
tance, Om,  from  pole  to  the  point  of 
application,  m  of  the  horizontal 
thrust ;  b,  the  horizontal  distance 
between  the  centre  of  gravity  of  the 
segment  E  F  I  K  C  and  the  vertical 
through  C  ;  A,  the  area  of  the  seg- 
ment ;  v,  the  variable  angle  nQm,  FlQ 
and  7-,  the  variable  distance  On. 

For  equilibrium,  considering  w  equal  to  unity,  we  have 
H  (r'  —  r  cos  v)  =  A  (r  sin  v  —  J), 

whence  r  =        .    r  +  .     .    .    .     (153) 

A  sin  v  -f  H  cos  v 

Assuming  any  joint,  the  corre'sponding  values  of  A  and  b 
for  this  joint  are  easily  calculated.  These  being  substituted, 
and  H  and  v  being  known,  the  corresponding  value  of  r  is 
deduced.  The  curve  may  then  be  constructed  by  points. 

A  simple  inspection  of  the  curve  of  resistance  will 
show  where  the  weak  points  of  the  arch  are,  where  the 
heaviest  strains  are  exerted,  and  where  the  joints  tend  to 
open,  whether  on  the  soffit  or  on  the  back. 

316.  The  deviation  of  the  curve  of  pressure  from  the  curve 
of  resistance  is  not  great,  and  no  material  error  is  ordinarily 
made  when  the  points  of  the  curve  of  pressure  cut  by  the 
joints  are  taken  as  the  centres  of  pressure  for  the  joints. 

In  arches  with  the  ordinary  form  of  voussoirs,  the  curve  of 
pressure  lies  below  the  curve  of  resistance,  and  the  condition 
that  it  shall  lie  within  the  middle  third  of  the  joints  is 
favorable  to  the  stability  of  the  arch. 


236  CIVIL    ENGINEERING. 

When  the  weight  of  the  voussoirs  and  the  load  on  the 
arch  are  determined,  as  in  Art.  313,  by  considering  them  com- 
posed of  vertical  laminae,  the  curves  of  pressure  and  of  re- 
sistance will  coincide  with  each  other. 

Economy  of  material  would  indicate  that  the  intrados  and 
extrados  should  be  similar  curves. 

317.  Depth  of  keystone.— The  form  of  the  arch  being 
assumed,  the  next  step  is  to  fix  its  thickness  or  depth.  The 
power  of  the  arch  to  resist  the  horizontal  thrust  at  the  crown 
will  depend  upon  the  strength  of  the  material  of  which  it  is 
made  and  upon  the  vertical  thickness  (depth)  of  the  key. 

The  pressure  at  the  extrados  of  the  key,  which  in  general 
is  the  most  exposed  part  of  the  joint,  should  not  exceed  -fa 
the  ultimate  strength  of  the  material.  Admitting  that  the 
centre  of  pressure  on  this  joint  may  be  at  one-third  of  the 
length  of  the  joint  from  the  extrados,  we  see  that  in  order 
to  keep  within  this  limit  of  -j^,  the  mean  pressure  should  not 
exceed  fa. 

The  celebrated  Ferronnet  gave  a  rule  for  determining  the 
thickness  or  depth  of  the  key,  which  is  very  nearly  expressed 
by  the  following  formula : 

'   d  =  T£  +  °'33 (154) 

dj  the  depth  in  metres ;  and 

7*,  the  radius  of  the  semicircle,  or  intrados,  in  same  unit. 
Gen.  Wood  bury  expressed  this  rule  as  follows : 
d  =  13  inches  +  -fa  the  span. 

For  arches  with  radius  exceeding  15  metres,  this  rule  gives 
too  great  a  thickness. 
Prof.  Rankine  gives 

d=  V.12r, 

in  which  r  is  the  radius  of  curvature  at  the  crown  in  feet. 
His  rule  is,  "  For  the  depth  of  the  keystone,  take  a  mean  pro- 
portional between  the  radius  of  curvature  of  the  intrados  at 
the  crown  and  a  constant  whose  value  for  a  single  arch  is  .12 
feet." 

He  recommends,  however,  in  actual  practice,  to  take  a 
depth  founded  on  dimensions  of  good  examples  already  built. 

318.  Thickness  of  piers  and  abutments.— The  stability 
of  these  may  be  considered  by  regarding  them  either  as  con- 
tinuations of  the  arch  itself  clear  to  the  foundation,  or  as  walla 
whose  moment  about  the  axis  of  rotation  is  greater  than  the 
moment  of  the  thrust  of  the  arch. 


THICKNESS   OF   ABUTMENTS. 


237 


In  either  case,  the  student  will  be  ablej  by  applying  the 
principles  already  discussed,  to  determine  the  dimens.ons 
necessary  to  give  the  pier,  in  order  that  its  moment  around 
any  edge  shall  exceed  the  moment  of  the  thrust  around  the 
same  axis. 

The  factor  of  safety  is  taken  at  about  2.  In  piers  of  great 
height  this  factor  should  be  increased,  while  for  small  heights 
it  may  be  reduced. 

319.  Thickness  of  abutment  and  depth  of  keystone 
for  small  arches. 

The  following  empirical  table  is  deduced  from  actual  ex- 
amples, and  may  be  used  for  small  arches  if  made  of  first- 
class  masonry: 

TABLE. 


Bpanin 
feet 

Thickness  of  Abutment—  for  heights  of 

Depth  of  key- 
stone in  inches. 

10  feet. 

15  feet. 

20  feet. 

25  feet. 

10 

5 

6 

7 

8 

14 

20 

6 

7 

8 

9 

19 

25 

*} 

7i 

8| 

H 

20 

30 

7 

8 

9 

10 

21 

35 

7* 

8| 

w 

10* 

22 

40 

8 

9 

10 

11 

23 

45 

Si 

9i 

10) 

111 

24 

50 

9 

10 

11 

12 

25 

If  the  masonry  be  second-class,  or  be  roughly  dressed,  the 
depth  of  the  keystone  should  be  increased  about  one-fourth. 


Form  of  Cylindrical  Arches. 

320.  As  stated  before,  these  arches  may  be  full  centre, 
segmental,  elliptical,  or  oval. 

Full  centre  arches  offer  the  advantages  of  simplicity  of 
form,  great  strength,  and  small  lateral  thrust.  But  where  the 


238 


CIVIL   ENGINEERING. 


span  is  considerable,  they  require  a  correspondingly  great 
rise,  which  is  often  objectionable. 

The  segmental  arch  enables  us  to  reduce  the  rise,  but 
causes  a  greater  lateral  thrust  on  the  abutments. 

The  oval  affords  a  means  of  avoiding  both  the  great  rise 
and  the  great  lateral  thrust,  and  gives  a  curve  of  pleasing 
appearance. 

Rampant  and  Inverted  Arches. 

321.  The  arch  in  the  preceding  cases  has  been  supposed  to 
have  been  upright,  and  either  right  or  oblique.     Rampant 
arches  are  frequently  used ;  sometimes  the  axis  is  even  verti- 
cal.    A  retaining  wall  with  a  semi-circular  horizontal  section 
would  be  an  example.     Arches  are  often  constructed  with 
their  soffits  forming  the  upper  side.     These  are  frequently 
used  under  openings,  their  object  being  to  distribute  the 
weight  equally  over  the  substructure  or  along  the  founda- 
tions.    They  are  known  as  inverted  arches,  or  inverts.     The 
principles  already  laid  down  for  the  upright   arch  apply 
equally  to  them. 

Wooden  Arches. 

322.  This  term,  -wooden  arch,  is  quite  often  Applied  to  a 
beam  bent  to  a  curved  shape,  its  ends  being  conimed  so  that 
the  beam  cannot  resume  its  original  form.     In  this  shape  the 
beam  possesses  under  a  load  greater  stiffness  than  when  it  is 
straight. 

A  single  beam  may  be  used  for  narrow  spans,  but  built 
beams,  either  solid  or  open,  must  be  used  for  wide  ones. 


FIG.  106. 


The  load  they  support  rests  upon  the  ty  p  of  the  beams,  as 
•diown  in  Fig.  106,  or  is  suspended  from  hem.  as  shown  in 
Fig.  107. 


RUBBLE   WALLS. 


239 


Although  called  arches,  they  are  so  only  in  form,  as  they 
are  not  composed  of  separate  pieces  held  in  place  by  mutual 
pressure.  They  are  now  more  generally  called  by  their 
proper  name,  curved  beams. 

If  we  assume  that  the  beam  resists  by  compression  alone, 
the  dimensions  of  the  beam  can  be  easily  determined,  in  terms 
of  the  load,  of  the  rise,  and  the  span. 


FIG.  107. 

GRAPHICAL  METHOD  OF  INVESTIGATION. 

323.  The  graphical  method  by  means  of  the  curve  of  equi- 
librium is  a  method  much  used  at  the  present  time  for  obtain- 
ing the  strains  on  the  different  parts  or  the  arch. 

This  method  of  investigation  will  be  alluded  to  in  a  future 
article. 


CHAPTER  X. 

CONSTRUCTION  OF  MASONRY. 
WALLS  OF  STRUCTURES. 

Stone-masons  class  the  methods  of  building  walls  of  stone 
into  rubble  work  and  ashlar  work. 

L  Rubble  Work. 

324.  The  stones  used  are  of  different  sizes  and  shapes,  pre- 
pared by  knocking  off  all  sharp,  weak  angles  of  the  blocks  with 
a  hammer.  They  are  laid  in  the  wall  either  dry  or  in  mortar. 
If  laid  without  reference  to  their  heights,  tne  masonry  is 
known  as  uncoursed  rubble,  or  common  rubble  masonry. 


240  CIVIL   ENGINEERING. 

In  building  a  -wall  of  rubble  (Fig.  108)  the  mason  must 
be  careful  to  place  the  stones  so  that  they  may  fit  one  upon 
the  other,  filling  the  interstices  between  the  larger  stones  by 
smaller  ones.  Care  should  be  taken  to  make  the  vertical 
courses  break  joints. 

If  mortar  is  used,  the  bed  is  prepared  by  spreading  mortar 
over  the  top  of  the  lower  course,  and  in  this  bed  the  stone 
is  firmly  imbedded.  The  interstices  are  filled  with  smaller 


FIG.  108. 

stones,  or  stone  chippings,  and  mortar,  and  finally  the  whole 
course  grouted. 

The  mean  thickness  of  a  rubble  wall  should  not  be  less 
than  one-sixth  of  the  height ;  in  the  case  of  a  dry  stone  wall, 
the  thickness  should  never  be  less  than  two  feet.  It  strengthens 
the  wall  very  much  to  use  frequently  in  every  course,  stones 
which  pass  entirely  through  the  wall  from  the  front  to  the 
back.  These  are  called  throughs.  If  they  extend  only  part 
of  this  distance,  they  are  called  binders. 

325.  Coursed  rubble,  or  hammered  masonry. — When  the 
stones  are  laid  in  horizontal  courses,  and  each  course  levelled 
throughout  before  another  is  built  upon  it,  the  work  is  termed 
coursed  rubble.  As  this  requires  the  stones  to  be  roughly 
dressed,  or  hammered  into  regular  forms  before  they  are  laid, 
the  work  is  frequently  called  hammered,  or  dressed  rubble. 
The  same  care  should  be  taken  in  building  masonry  of  this 
kind  as  that  required  for  common  rubble.  The  mason  must 
be  particular  in  making  the  upper  and  lower  surfaces  of  each 
stone  parallel,  and  when  laying  the  stones  to  keep  a  uniform 
height  throughout  each  course.  If  a  stone  in  the  course  is 
not  high  enough,  other  stones  are  laid  on  it  till  the  required 
height  is  obtained. 

The  different  courses  are  not  all  of  the  same  height,  but 
vary  according  to  the  size  of  the  stone  used.  The  only  condi- 
tion required  is  that  each  course  shall  be  kept  of  the  same 
height  throughout. 


ASHLAR   MASONRY. 


241 


At  the  corners,  stones  of  large  size,  and  more  acurately 
dressed,  are  used.  These  are  known  as  quoins,  and  are  laid 
with  care,  serving  as  gauges  by  which  the  height  of  the  course 
is  regulated. 


n.  Ashlar  Work. 

326.  The  stones  in  this  kind  of  masonry  are  prepared  by 
having  their  beds  and  joints  accurately  squared  and  dressed. 
They  are  made  of  various  sizes  depending  on  the  kind  of 
wall  to  be  built  and  the  size  of  the  blocks  produced  by  the 
quarry.  Ordinarily  they  are  about  one  foot  thick,  two  or 
three  feet  long,  and  have  a  width  from  once  to  twice  the 
thickness.  They  are  used  generally  for  the  facing  of  a 
wall,  to  give  the  front  a  regular  and  uniform  appearance,  and 
where,  by  the  regularity  of  the  masses,  a  certain  architectural 
effect  is  to  be  produced. 

Ashlar  work  receives  different  names,  from  the  appearance 
of  the  face  of  the  "ashlar,"  and  from  the  kind  of  tool  used  in 
dressing  it.  If  the  block  be  smooth  on  its  face,  it  is  called 
plane  ashlar  (Fig.  109) ;  if  fluted  vertically,  tooled  ashlar  ; 


PIG.  109 — Represents  a  wall  with  facing  of  plane  ashlar. 


if  roughly  trimmed,  leaving  portions  to  project  beyond  the 
edges,  rustic  ashlar,  etc.,  etc.  Rustic  ashlar  is  known  as 
rustic,  rustic  chamfered,  rustic  work  frosted,  rustic  work 
vermiculated,  etc. 

Ashlars  are  laid  in  fine  mortar  or  cement.  Each  one  should 
be  first  fitted  in  its  place  dry,  so  that  any  inaccuracy  in  the 
dressing  may  be  discovered  and  corrected  before  the  stone  is 
finally  set  in  mortar. 

To  provide  for  a  uniform  bearing  the  stone  should  be  ac- 
curately squared.     Frequently  the  bed  is  made  to  slant  down 
16 


242 


CIVIL   ENGINEERING. 


wards,  from  front  to  back,  for  the  purpose  of  making  close 
horizontal  joints  in  front.  This  weakens  the  stone,  as  the 
weight  is  thrown  forward  on  the  edges  of  the  stones,  which 
chip  and  split  off  as  the  work  settles. 

327.  Walls  built  with  ashlar  facing  are  backed  with  brick 
or  rubble.  Economy  will  decide  which  is  to  be  used.  In  the 
construction,  throughs  of  ashlars  should  be  used  to  bind  the 
backing  to  the  facing.  Their  number  will  be  proportioned  to 
the  length  of  the  course.  The  vertical  courses  break  joints, 
each  vertical  joint  being  as  nearly  as  possible  over  the  middle 
of  the  stone  below. 


Fig.  110  —  Represents  a  section  of  wall  with  facing  of  ashlar  and  a  back- 

ing of  rubble. 


When  the  backing  is  rubble,  the  method  of  slanting  the 
may  be  allowed  for  the  purpose  of  forming  a  better  bond 
between  the  rubble  and  ashlar  ;  but,  even  in  this  case,  the 
block  should  be  dressed  true  on  each  joint,  to  at  least  one  foot 
back  from  the  face.  If  there  exists  any  cause  which  would 
give  a  tendency  to  an  outward  thrust  from  the  back,  then, 
instead  of  slanting  off  all  the  blocks  towards  the  tail,  it  will  be 
preferable  to  leave  the  tails  of  some  thicker  than  the  parts 
which  are  dressed. 

Cut-stone  Masonry. 

328.  Where  great  strength  is  required  in  the  wall,  each 
stone  is  prepared  by  cutting  it  to  a  particular  shape,  so  that 
it  can  be  exactly  fitted  in  the  wall  ;  masonry  of  this  kind  is 
called  cut-stone.  In  other  words,  every  stone  is  an  ashlar  ; 


STRENGTH   OF   MASONET.  243 

hence  the  terms   cut-stone  and  ashlar  masonry    are  often 
used  one  for  the  other. 

Cut-stone  masonry,  when  carefully  constructed,  is  more 
solid  and  stronger  than  any  other  class.  The  labor  required 
in  preparing  the  blocks  makes  it  the  most  expensive.  It  is, 
therefore,  restricted  in  its  use  to  those  structures  where 
great  strength  is  indispensable. 


Stone-cutting. 

329.  The  usual  method  of  dressing    a   surface  is  to  cut 
draughts  around  and  across  the  stone  with  a  chisel,  and  then 
work  down  the  intermediate  portions  between  the  draughts  by 
the  use  of  proper  tools.  The  latter  are  usually  the  chisel,  axe, 
and  hammer. 

No  particular  difficulty  occurs  in  working  a  block  of  stone, 
the  faces,  beds,  and  joints  of  which  are  to  be  plane  or  even 
cylindrical  surfaces ;  the  only  difference  in  method  for  the 
two  being  that  a  curved  rule  is  used  in  one  direction  and  a 
straight  one  in  another  for  the  cylindrical  surface,  while  for 
the  plane  surface  only  one  rule  is  used. 

If  the  surfaces  are  to  be  conical,  spherical,  or  warped,  the 
operation  is  more  difficult.  It  becomes  necessary  to  bring  the 
block  to  a  series  of  plane  or  cylindrical  surfaces,  and  then 
reduce  them  to  the  required  form.  To  show  how  this  can  be 
done  with  the  least  waste  of  material  is  one  of  the  objects  of 
-  stereotomy  .* 

Strength  of  Masonry. 

Strength. — The  strength  of  masonry  will  depend  on  the 
size  of  the  blocks,  on  the  accuracy  of  the  dressing,  and  on 
the  bond. 

330.  Size  of  stone. — The  size  of  the  blocks  varies  with  the 
kind  of  stone  and  the  nature  of  the  quarry. 

Some  stones  are  of  a  strength  so  great  as  to  admit  of  their 
being  used  in  blocks  of  any  size,  while  others  can  only  be  used 
with  safety  when  the  length,  breadth,  and  thickness  of  the 
block  bear  certain  relations  to  each  other. 

The  rule  usually  followed  by  builders,  with  ordinary  stone, 
is  to  make  the  breadth  at  least  equal  to  the  thickness,  and 
seldom  greater  than  twice  this  dimension,  and  to  limit  the 
length  to  within  three  times  the  thickness.  When  the  breadth 
or  the  length  is  considerable  in  comparison  with  the  thick 


244  CIVIL   ENGINEERING. 

ness,  there  is  danger  that  the  block  may  break,  if  any  unequal 
settling  or  unequal  pressure  should  take  place.  As  to  the  ab- 
solute dimensions,  the  thickness  is  generally  not  less  than  one 
foot,  nor  greater  than  two ;  stones  of  this  thickness,  with  the 
relative  dimensions  just  laid  down,  will  weigh  from  1,000  to 
8,000  pounds,  allowing,  on  an  average,  160  pounds  to  the 
cubic  foot.  With  these  dimensions,  therefore,  the  weight  of 
each  block  will  require  a  very  considerable  power,  both  of 
machinery  and  men,  to  set  it  on  its  bed. 

From  some  quarries  the  formation  of  the  stone  will  allow 
only  blocks  of  medium  or  small  size  to  be  furnished,  while 
from  others  stone  of  almost  any  dimensions  can  be  obtained. 

331.  Accuracy  of  dressing. — The  closeness  with  which 
the  blocks  fit  is  solely  dependent  on  the  accuracy  with  which 
the  surfaces  in  contact  are  wrought  or  dressed ;  if  this  part  of 
the  work  is  done  in  a  slovenly  manner,  the  mass  will  not  only 
open  at  the  joints  with  an  inequality  in  the  settling,  but,  from 
the  courses  not  fitting  acurately  on  their  beds,  the  blocks  will 
be  liable  to  crack  from  the  unequal  pressure  on  the  different 
points  of  the  block. 

To  comply  with  the  first  of  the  general  principles  to  be 
observed  in  the  construction  of  masonry,  we  should  have,  in  a 
wall  supporting  a  vertical  pressure,  the  surfaces  of  one  set  of 
joints,  the  beds,  horizontal.  This  arrangement  will  prevent 
any  tendency  of  the  stones  to  slip  or  slide  under  the  action  of 
the  weight  they  support. 

The  surfaces  of  the  other  set  should  be  perpendicular  to 
the  beds,  and  at  the  same  time  perpendicular  to  the  face,  or  to 
the  back  of  the  wall,  according  to  the  position  of  the  stones  in 
the  mass  ;  two  essential  points  will  thus  be  attained  ;  the  angles 
of  the  blocks  at  the  top  and  bottom  of  the  course,  and  at  the 
face  or  back,  will  be  right  angles,  and  the  block  will  therefore 
be  as  strong  as  the  nature  of  the  stone  will  admit. 

The  greater  the  accuracy  of  the  dressing,  the  more  readily 
can  these  surfaces  be  made  to  fulfil  these  conditions. 

When  a  block  of  cut  stone  is  to  be  laid,  the  first  point  to  be 
attended  to  is  to  examine  the  dressing,  by  placing  the  block 
on  its  bed,  and  seeing  that  the  face  is  in  its  proper  plane,  and 
that  the  joints  are  satisfactory.  If  it  be  found  that  the  fit  is 
not  accurate,  the  inaccuracies  are  marked,  and  the  requisite 
changes  made. 

332.  Bond. — Among  the  various  methods  used,  the  one 
known  as  headers  and  stretchers  is  the  most  simple,  and 
offers,  in  most  cases,  all  requisite  solidity;  in  this  method  the 
vertical  joints  of  the  blocks  of  each  course  alternate  with  the 


BOND. 


245 


rertical  joints  of  the  courses  above  and  below  it,  or  break 
joints  with  them,  and  the  blocks  of  each  course  are  laid  alter- 
nately with  their  greatest  and  least  dimensions  to  the  face  of 
the  wall ;  those  which  present  the  longest  dimension  along  the 
face  are  termed  stretchers,  the  others  headers.  (Fig.  111.) 


[_         151 

1    , 

1        1 

1      1 

FIG.  Ill — Represents  an  elevation 
A,  vertical  section  B,  and  horizontal 
section  C,  of  a  wall  arranged  as 
headers  and  stretchers. 

a,  stretchers. 

5,  headers. 


1 

- 

1                1 

!                        7 

I    •*    i6 

By  arranging  the  blocks  in  this  manner  the  facing  and 
backing  of  each  course  are  well  connected  ;  and,  if  any  une- 
qual settling  takes  place,  the  vertical  joints  cannot  open,  as 
would  be  the  case  were  they  continuous  from  the  top  to  the 
bottom  of  the  mass,  for  each  block  of  one  course  confines  the 
ends  of  the  two  blocks  on  which  it  rests  in  the  course  beneath. 


FIG.  112— Represents  an  elevation  A,  and  perspective  views  C  and  D,  of 
two  of  the  blocks  of  a  wall  in  which  the  blocks  are  fitted  with  indente, 
and  connected  with  bolts  and  cramps  of  metal. 


246 


CIVIL   ENGINEERING. 


333.  In  masonry  exposed  to  violent  shocks,  the  blocks  of 
each  course  require  to  be  not  only  very  firmly  united  with 
each  other,  but  also  with  the  courses  above  and  below  them. 
To  effect  this  various  means  have  been  used.  Sometimes  the 
stones  of  different  courses  are  connected  by  tabling,  which 
consists  in  having  the  beds  of  one  course  arranged  with  pro- 
jections (Fig.  112)  which  fit  in  corresponding  indentations 
of  the  next  course.  Iron  cramps  in  the  form  of  the  letter  S, 
set  with  melted  lead,  are  often  used  to  confine  two  blocks  to- 
gether. Holes  are,  in  some  cases,  drilled  through  several 
courses,  and  the  blocks  of  these  courses  are  connected  by 
strong  iron  bolts  fitted  to  the  holes. 

Light-houses,  in  exposed  positions,  are  peculiarly  liable  to 
violent  shocks  from  the  waves.  They  are  ordinarily,  when 
thus  exposed,  built  of  masonry,  are  round  in  cross-section,  and 
solid  up  to  the  level  of  the  highest  tide.  The  stones  are  often- 
times dove-tailed  and  dowelled  into  each  other,  as  well  as 
fastened  together  by  metal  bolts  and  cramps. 

The  manner  of  dove-tailing  the  stones  is  shown  in  plan  in 
Fig.  113,  which  represents  part  of  a  course  where  this  method 
is  used. 


FIG.  113. 


The  chief  use  of  the  dove-tailing  is  to  resist  the  tendency  of 
the  stones  to  jump  out  immediately  after  receiving  the  blow 
of  the  wave.  This  method  was  first  used  by  Smeaton  in  build- 
ing the  Eddystone  light-house.  The  light-house  on  Minot'a 
Ledge,  Massachusetts  Bay,  built  under  the  superintendence 
of  General  B.  S.  Alexander,  U.  S.  Corps  of  Engineers,  by 
the,  Light-House  Board,  is  a  good  example  of  the  bond  and 
metal  fastenings  used  in  such  structures.  (Figs.  114  and 
115.) 


BOND. 


247 


FIG    114.— Vertical  section  showing  foundation  courses,  metal  fastenm**, 
and  the  first  story  above  the  foundation  courses. 


Kio  115._Plan   of  twenty-second  course,  showing  the  method  of 
tailing  the  stones- 


248  CIVIL   ENGINEERING. 


Machinery  used  in  Constructing  Walls  of  Stone. 

334.  Scaffolding1.— In  building  a  wall,  after  having  raised 
it  as  high  as  it  can  be  conveniently  done  from  the  ground, 
arrangements  must  be  made  to  raise  the  workmen  higher,  so 
that  they  can  continue  the  work.     This  is  effected  by  means 
of  a  temporary  structure  called  scaffolding. 

If  the  wall  is  not  used  to  afford  a  support  for  the  scaffold- 
ing, two  rows  of  poles  are  planted  firmly  in  the  ground,  par- 
allel to  the  wall,  and  about  four  and  a  half  feet  apart.  These 
uprights  in  each  row  are  from  twelve  to  fourteen  feet  apart, 
and  from  thirty  to  forty  and  even  fifty  feet  in  height,  depend- 
ing upon  how  high  the  wall  is  to  be  built. 

Horizontal  pieces  are  then  firmly  fastened  to  the  uprights, 
having  their  upper  surfaces  nearly  on  the  same  level  as  the 
highest  course  of  masonry  laid.  Cross  pieces  or  joists  are 
laid  on  these,  and  upon  them  a  flooring  of  boards.  Upon 
this  platform  the  masons  place  their  tools  and  materials  and 
continue  the  work. 

As  the  wall  rises  other  horizontal  pieces  are  used,  and  the 
joists  and  boards  carried  to  the  new  level.  Diagonal  pieces 
are  used  between  the  rows  to  brace  them  together,  and  in 
each  row  to  stiffen  the  supports. 

The  workmen  ascend  the  scaffolding  by  means  of  ladders. 
The  materials  are  hoisted  by  means  of  machinery  placed  on 
the  scaffolding  or  detached  from  it. 

335.  Crane. — The  movable  or  travelling  crane,  which  is 
so  arranged  as  to  admit  of  being  moved  in  the  direction  of 
the  scaffolding  and  across  it,  is  often  used  on  the  scaffolding 
for  hoisting  the  stone. 

Shears,  which  consist  of  two  or  more  spars  or  stout  pieces 
of  timber,  fastened  together  near  the  top,  and  f urnished  with 
blocks  and  tackles,  are  sometimes  used. 

The  kind  of  machinery  to  be  used  in  hoisting  the  stone 
will  be  determined  by  the  size  of  the  blocks  to  be  lifted,  the 
magnitude  and  character  of  the  work,  and  the  suitability  of 
the  site. 

In  the  United  States,  the  machine  known  as  the  "  boom 
derrick,"  or  simply  "  derrick,"  a  modified  form  of  crane,  is 
much  used  in  works  of  magnitude. 

In  the  example  shown  in  Fig.  116,  the  mast  is  held  in  a 
vertical  position  by  four  guys,  generally  wire  ropes,  fastened 
to  a  ring  on  the  iron  cap  which  is  fitted  to  the  top  of  the 


HOISTING   MACHINERY. 


249 


mast.     Below  this  ring,  and  revolving  freely  on  the  cap,  is 
a  wrought-iron  frame  containing  two  sheaves  or  pulleys. 

The  "  boom,"  or  derrick,  has  its  outer  end  supported  by  a 
topping-lift  fastened  to  this  wrought-iron  frame.  The  other 
end  fits  into  an  iron  socket  with  collar,  or  is  fastened  to  a 
wooden  frame  which  embraces  the  mast,  and  has  a  motion  of 
rotation  around  it.  The  wooden  frame  bears  two  windlasses 
and  a  platform  on  which  the  men  stand  while  working  them. 
Two  tackles  are  used,  one  suspended  from  the  outer  end  of 
the  boom,  the  other  from  the  mast-head,  the  falls  of  both 
leading  over  the  sheaves  and  thence  to  the  windlasses. 


FIG.  116. 


The  lower  blocks  of  the  tackles  are  fastened  to  a  triangular 
plate  from  which  a  hook  is  suspended.  It  is  seen  that  by 
hauling  upon  or  slacking  the  falls  alternately,  the  stone  sus- 
pended from  the  triangular  plate  can  be  placed  at  any  point 
within  the  circle  described  by  the  outer  end  of  the  boom. 

336.  The  blocks  of  stone  are  attached  to  the  tackle  in 
various  ways.  Some  of  the  most  usual  methods  are  as  fol- 
lows: 

I.  By  nippers  or  tongs,  the  claws  of  which  enter  a  pair  of 
holes  in  the  sides  of  the  stone. 

IL  By  two  iron  pins  let  into  holes,  which  they  closely  fit, 


250 


CIVIL   ENGINEERING. 


sloping  towards  each  other  (Fig.  117).     The  force  applied  to 
the  chain  to  lift  the  block,  jams  the  pins  in  their  holes. 


FIG.  117— Represents  a  perspective  view  of  the  tackling  for  hoisting  a 
block  of  stone,  A,  with  draughts  around  the  edges  of  its  faces,  and  th« 
intermediate  space  axed  or  knotted. 

a,  draughts  around  edge  of  block. 

6,  knotted  part  between  draughts. 

c,  iron  bolts  with  eyes  let  into  oblique  holes  cut  in  the  block. 

d  and  e,  chain  and  rope  tackling. 

III.  By  a  simple  contrivance  made  of  three  pieces  of  iron, 
called  a  lewis  (Fig.  118),  which  has  a  dove- tail  shape,  with 
the  larger  end  downwards,  fitting  in  a  hole  of  similar  shape. 
The  depth  of  the  hole  depends  upon  the  weight  and  the  kind 
of  stone  to  be  raised.  The  tapering  side-pieces,  n,  n,  of  the 
lewis  are  inserted  and  placed  against  the  sides  of  the  hole ; 
the  middle  piece,  0,  is  then  inserted  and  secured  in  its  place 
by  a  pin.  The  stone  is  then  safely  hoisted,  as  it  is  impossible 
for  the  lewis  to  draw  out  of  the  hole. 


FIG.  118 — Represents  the  com- 
mon iron  lewis  B. 

n,  n,  side  pieces  of  the  lewis. 

o,  centre  piece  of  lewis,  with 
eye  fastened  to  n,  n  by  a  bolt. 

P,  iron  ring  for  attaching  tackling. 


FIG.  119— A  line  attached  to 
the  straight  piece,  &,  admits 
of  the  latter  being  drawn 
out,  allowing  the  piece,  », 
to  be  removed. 


Where  it  may  not  be  convenient  to  reach  the  pin  after  the 
Btone  has  been  placed  in  position,  a  lewis  of  the  form  showd 
in  (Fig.  119)  may  be  used. 


BOND.  25  J 


WALLS   OF   BEIOK. 

337.  Bricks  have  been  referred  to  in  a  previous  chapter 
as  artiiicial  stones.      It  therefore  follows  that  the  general 
principles  enunciated  for  the  construction  of  stone  masonry 
are  the  same  for  brick  as  far  as  they  are  applicable. 

From  the  uniformity  of  size  of  brick,  builders  describe  the 
thickne&s  of  a  wall  by  the  number  of  bricks  extending  across 
it.  ^  Thus,  a  wall  formed  of  one  thickness  of  brick  lying  on 
their  broad  side,  with  their  length  in  the  direction  of  the 
length  of  the  wall,  is  said  to  be  "  half  brick  thick."  If  the 
thickness  of  the  wall  is  equal  to  the  length  of  one  brick,  the 
wall  is  called  "  one  brick  thick,"  etc. 

The  bond  used  depends  upon  the  character  of  the  struc- 
ture. The  most  usual  kinds  are  known  as  the  English  and 
Flemish. 

338.  English  bond. — This  consists  in  forming  each  course 
entirely  of  headers  or  of  stretchers,  as  shown  in  Fig.  120. 

Sometimes  the  courses  of  headers  and  stretchers  occur 
alternately ;  sometimes  only  one  course  of  headers  for  three 
or  four  courses  of  stretchers.  The  effect  of  the  stretchers  is 
to  tie  the  wall  together  lengthwise,  and  the  headers,  cross- 


I       I       I 


I       I       I       I       I 


I.    .1.     I.    .1 


I       I      I       I 


Fig.  120. 

wise.  The  proportionate  number  of  courses  of  headers  to 
those  of  stretchers  depend  upon  the  relative  importance  of 
the  transverse  and  longitudinal  strength  in  the  wall. 

Since  the  breadth  of  a  brick  is  nearly  equal  to  half  its 
length,  it  would  be  impossible,  beginning  at  a  vertical  end  or 
angle,  to  make  this  bond  with  whole  bricks  alone.  This 
difficulty  is  removed  by  the  use  of  a  half-brick,  made  by 
cutting  a  brick  in  two  longitudinally.  A  whole  brick,  useu 
as  a  header,  is  placed  at  the  corner;  next  to  this  is  put  a 


SJ52  CIVIL   ENGINEERING. 

half -brick.  This  allows  the  next  header  to  make  the  neces- 
sary overlap,  which  can  be  preserved  throughout  the  course. 
These  half-bricks  are  called  closers. 

339.  Flemish  "bond. — This  consists  in  laying  headers  and 
stretchers  alternately  in  each  course. 

A  wall  built  with  this  bond  presents  a  neater  appearance 
than  one  built  in  English  bond,  and  is,  therefore,  generally 
preferred  for  the  fronts  of  buildings.  It  is  not  considered 
as  strong  as  the  English,  owing  to  there  being,  ordinarily,  a 
less  number  of  headers  in  it. 

840.  Strengthening  of  bond. — Pieces  of  hoop-iron  or  iron 
lath,  so  thin  that  they  may  be  inserted  in  the  joints  without 
materially  increasing  their  thickness,  add  to  the  strength  of 
the  bond,  especially  when  hydraulic  mortar  is  used.  They 
are  laid  flat  in  the  bed-joints,  and  should  break  joints.  It  is 
well  to  nick  them  at  intervals  and  bend  the  ends  at  right 
angles  for  the  length  of  two  inches,  inserting  the  bent  ex- 
tremities into  the  vertical  joints. 

This  method  was  used  by  Brunei  in  forming  the  entrance 
to  the  Thames  tunnel,  and  is  sometimes  designated  as 
hoop  iron  bond. 

341.  Hollow  masonry. — Hollow  brick  walls  are  now  ex- 
tensively used  in  buildings. 

The  advantages  of  hollow  walls  are  economy,  lightness, 
and,  particularly,  freedom  from  dampness. 

The  bricks  may  be  hollow,  being  laid  in  the  usual  way,  but 
the  usual  method  of  forming  the  walls  is  to  use  ordinary  brick, 
and  so  arrange  them  in  the  walls  as  to  leave  hollow  spaces 
where  required. 

342.  Strength  of  brick  masonry. — The  strength  of  brick 
masonry  depends    upon   the   same   three   conditions  already 
given  for  stone.     Hence,  all  misshapen  and  unsound  bricks 
should  be  rejected. 

With  good  bricks  and  good  mortar  a  masonry  of  strength 
and  durability  nearly  equal  to  rtone  is  easily  formed,  and  at 
less  cost.  Its  strength  is  largely  due  to  the  strong  adhesion 
of  mortar  to  brick.  The  volume  of  mortar  used  is  about  one- 
fifth  that  of  the  brick. 

343.  Laying  the  bricks. — The  strength  of  brick  masonry 
is  materially  affected  by  the  manner  in  which  the  bricks  are 
laid.     They  should  not  only  be  placed  in  position,  but  pressed 
down  firmly  into  their  beds. 

As  bricks  have  great  avidity  for  water,  it  would  always  be 
well  not  only  to  moisten  them  before  laying,  but  to  allow 
them  to  soak  in  water  several  hours  before  they  are  used 


CONCRETE   WALLS. 

By  taking  this  precaution,  the  mortar  between  the  joints  will 
set  more  firmly. 

To  wet  the  bricks  before  they  were  carried  on  the  scaffold 
would,  by  making  them  heavier,  add  materially  to  the  labor 
of  carrying,  It  is  suggested  to  have  arrangements  on  the 
scaffold  where  they  can  be  dipped  into  water,  and  then 
handed  to  the  mason  as  he  requires  them.  The  wetting  is  of 
great  importance  when  hydraulic  mortar  or  cement  is  used, 
for  if  the  bricks  are  not  wet  when  laid,  the  cement  will  not 
attach  itself  to  them  as  it  should. 


Machinery  of  Construction. 

34A.  Scaffolding. — In  ordinary  practice  the  scaffolds  are  car- 
ried up  with  the  walls,  and  are  made  to  rest  upon  them.  The 
essential  features  are  the  same  as  those  used  for  stone  walls. 
It  would,  be  an  improvement  if  an  inner  row  of  uprights  were 
used  instead  of  the  wall  to  support  the  framework,  for  the 
cross-pieces,  resting  as  they  often  do  on  a  single  brick  in  a 
green  wall,  must  exert  an  injurious  influence  on  the  wall. 

Machinery  for  hoisting  the  bricks,  mortar,  etc.,  are  used  in 
extensive  works.  For  ordinary  buildings  the  materials  are 
carried  up  by  workmen  by  means  of  ladders. 


WALLS   OF   CONCRETE. 

345.  Concrete  masonry. — "Within  recent  years  much  at- 
tention has  been  paid  to  the  construction  of  walls  entirely  of 
concrete. 

Method  of  construction. — The  concrete  is  moulded  into 
blocks,  as  previously  described,  and  then  laid  as  in  stone  ma- 
sonry ;  or  it  is  moulded  into  the  wall,  the  latter  becoming  a 
monolithic  structure. 

The  walls  in  the  latter  case  are  constructed  in  sections 
about  three  feet  high  and  ten  or  fifteen  long.  For  this  pur- 
pose a  mould  is  used  made  of  boards  forming  two  sides  of  a 
box,  the  interior  width  of  which  is  equal  to  the  thickness  of 
the  wall.  Its  sides  are  kept  in  place  by  vertical  posts,  which 
are  connected  together  and  prevented  from  spreading  apart 
by  small  iron  rods,  as  shown  in  Fig.  121. 

The  concrete  is  shovelled  into  the  mould  in  lavers  and 
rammed  with  a  pestle.  As  soon  as  the  mould  is  filled,  the 
iron  rods  are  withdrawn  and  the  mould  lifted  up.  A.  second 


254 


CIVIL   ENGINEERING. 


section  is  formed  in  like  manner  on  the  top  of  the  tirst,  and 

the  process  goes  on  until  the  wall  reaches  the  required  height. 

if  scaffolding  be  required  in  their  construction,  one  of  the 

ordinary  form  may  be  used,  or  one  like  that  shown  in  Fig.  121. 


Fig.  121. 

Tail's  bracket  scaffolding,  in  which  the  platforms  are 
sustained  by  clamping  them  to  the  wall  as  it  is  built  up, 
using  the  holes  left  when  the  iron  rods  are  withdrawn,  is  an 
example  of  one  of  the  devices  used  in  the  construction  of 
concrete  walls  ;  so  also  Clarke's  adjustable  frame,  in  which 
the  platform  is  supported  by  a  frame  from  above,  fastened  to 
clamps  embracing  the  wall.  Hoisting  apparatus  suitable  for 
the  work  is  also  employed. 

Hollow  -walls. — In  case  the  wall  is  required  to  be  hollow, 
a  piece  of  board  of  the  thickness  of  the  required  space  to  be 
left  open,  and  slightly  wedge-shaped  to  admit  of  its  being 
easily  removed,  is  laid  horizontally  in  the  mould,  and  the 
concrete  rammed  in  well  around  it.  When  the  concrete  is 
filled  to  the  top  of  the  board,  it  is  drawn  out,  leaving  the  re 


CROSS-SECTION^  OF   RETAINING   WALL.  255 

quired  air  space.     At  regular  intervals,  ordinary  bricks   are 
laid  as  ties  to  connect  together  the  outer  and  inner  walls. 

Fines,  pipes,  and  other  openings  for  heating,  ventilating, 
conveying  water,  gas,  smoke,  etc.,  are  constructed  in  a  similar 
manner  by  using  movable  cores  of  the  proper  size  and  form. 
Strength  and  advantages  of  concrete  -walls. — It  ia 
claimed  that  concrete  walls  are  easier  of  construction, 
cheaper,  and  stronger  than  brick  walls  of  the  same  thickness, 
and  that  they  possess  the  great  advantage  in  allowing  air  pas- 
sages and  flues  to  be  easily  constructed  of  uniform  size  and 
smooth  interiors. 


RETAINING  AND  RESERVOIR  WALLS. 

346.  Especial  care  should  be  taken,  in  the  construction  of 
these  walls,  to  secure  a  firm  foundation,  and  to  observe  all  the 
precautions  mentioned  in  previous  articles  for  laying  masonry. 

Thorough  drainage  must  be  provided  for,  and  care  be 
taken  to  keep  water  from  getting  in  between  the  wall  and  the 
earth.  If  the  water  cannot  be  kept  out,  suitable  openings 
through  the  masonry  should  be  made  to  allow  the  water  to 
escape. 

When  the  material  at  the  back  of  the  wall  is  clay,  or  is 
retentive  of  water,  a  dry  rubble  wall,  or  a  vertical  layer  of 
coarse  gravel  or  broken  stone,  at  least  one  foot  thick  horizon- 
tally, must  be  placed  at  the  back  of  the  retaining  wall,  be- 
tween the  earth  and  the  masonry,  to  act  as  a  drain. 

In  filling  in  the  earth  behind  the  wall,  the  earth  should  be 
well  rammed  in  layers  inclined  downward  from  the  wall. 

Especial  care  should  be  taken  to  allow  the  mortar  to  harden 
before  letting  the  wall  receive  the  thrust  of  the  earth. 

Whenever  it  becomes  necessary  to  form  the  embankment 
before  the  mortar  has  had  time  to  set,  some  expedient  should 
be  employed  to  relieve  the  wall  as  far  as  possible  from  pres- 
sure. Instead  of  bringing  the  embankment  directly  against 
the  back  of  the  wall,  dry  stone  or  fascines  may  be  interposed, 
or  a  stiff  mortar  of  clay  or  sand  with  about  ^th  in  bulk  of 
lime  may  be  used  in  place  of  the  dry  stone. 

347.  Form  of  cross-section  of  retaining  -walls. — The 
rectangular  and  the  trapezoidal  forms  are  the  most  common. 
It  is  usual,  in  the  latter  case,  to  give  the  face  a  batter,  varying 
between  -f-  and  \*,  and  to  build  the  back,  or  side  in  contact 
with  the  earth,  vertical,  or  in  steps.     From  experiments  mado 
with  models  of  retaining  walls,  it  was  shown  that  as  the  wall 


256 


CIVIL   ENGINEERING. 


gave  way,  the  prism  of  earth  pressing  against  it  did  not  revolve 
around  any  line,  but  settled  suddenly  and  then  rested  until 
another  shock.  These  experiments  seem  to  confirm  the  prac- 
tice of  building  the  back  in  steps. 

In  some  cases  the  wall  is  of  uniform  thickness  with  eloping 
or  curved  faces.     (Figs.  122  and  123.) 


FIG.  122. 


FIG.  123. 


It  will  be  seen  that,  the  weight  remaining  the  same,  the 
wall  with  sloped  or  curved  faces  has  an  increase  of  stability 
over  the  corresponding  equivalent  wall  of  rectangular  cross- 
section. 

The  advantage  of  such  forms,  therefore,  lies  in  the  saving 
of  material. 


FIG.  124. 


Walls  with  curved  batter  should  have  their  bed-joints  per- 
pendicular to  the  face  of  the  wall,  so  as  to  diminish  the  obli- 
quity of  pressure  on  the  base.  (Fig.  124.) 


AREAS,    LINTELS   AND   PLATE-BANDS. 


257 


348.  Counterforts. — Counterforts    are    generally    placed 
along  the  back  of  the  wall,  15  to  18  feet  apart,  from  centre  to 
centre;    their  construction   is  in  every  way  similar  to  that 
lecomrnended  for  retaining  walls. 

They  should  be  built  simultaneously  with  the  wall,  and  be 
well  bonded  into  it. 

349.  Relieving  arches. — The  name  of  relieving  arches 
is  given  to  a  range  of  arches  resting  against  the  back  of  a  re- 
taining wall  to  relieve  it  from  the  pressure, or  a  part  of  the 
pressure,  produced  by  the  earth  behind.     (Fig.  125.) 


FIG.  125. 

These  arches  have  their  axes  placed  at  right  angles  to  the 
back  of  the  wall,  and  may  have  their  fronts  enclosed  by  the 
earth,  as  shown  in  the  vertical  section  represented  in  Fig.  125. 
There  may  be  one  or  several  tiers  of  them. 

Knowing  the  natural  slope  of  earth  to  be  retained,  and 
assuming  the  length  of  the  arch,  its  height  can  be  deduced, 
or  assuming  the  height,  its  length  may  be  obtained,  so  that  the 
pressure  of  the  earth  on  the  wall  shall  not  exceed  a  given 
amount. 

The  distance  between  the  centres  of  relieving  arches  is 
ordinarily  about  18  or  20  feet.  The  thickness  of  the 
arch  and  piers  will  depend  upon  the  weight  they  have  to 
support. 

AREAS,  LINTELS,  ETC. 

350.  These  structures  sustaining  a  vertical  pressure  either 
upwards  or  downwards,  are  subjected  to  a  cross-strain. 

Area. — It  happens  sometimes  that  an  upward  pressure  is 
produced  on  an  area  by  the  presence  of  water ;  this  pressure 
must  be  guarded  against.  The  area  of  the  new  capitol  at 
17 


258  cmr,  ENGINEERING. 

Albany,  N.  Y.,  is  several  feet  thick,  and  was  made  by  first 
placing  large  flat  stones  over  the  surface,  and  then  adding 
successive  layers  of  broken  stone  and  concrete. 

Lintels. — The  resistance  to  a  transverse  strain  is  very  slight 
in  stone ;  therefore  the  distance  to  be  spanned  by  the  lintel 
should  be  quite  small,  seldom  exceeding  six  feet. 

Plate-bands. — For  a  similar  reason  to  that  just  given  for 
lintels,  the  span  of  a  plate-band  should  not  exceed  ten  feet, 
and  all  pressure  from  above  should  be  borne  by  some  inter 
posing  device. 


ARCHES. 

351.  The  form  of  the  arch  is  generally  assumed,  and  the 
number  and  thickness  of  the  voussoirs  are  determined  after- 
wards. The  curves  of  right  section  of  full  centre,  segmental, 
and  elliptical  arches  require  no  further  description,  as  the 
student  has  already  learned  the  method  of  constructing  these 
curves.  The  various  ovals  will  be  the  only  ones  described. 


Methods  of  Constructing  Ovals. 

352.  The  span  and  rise  of  an  arch  being  given,  together 
with  the  directions  of  the  tangents  to  the  curve  at  the  spring- 
ing lines  and  crown;  an  infinite  number  of  curves,  composed 
of  arcs  of  circles,  can  be  determined,  which  shall  satisfy  the 
conditions  of  forming  a  continuous  curve,  or  one  in  which  the 
arcs  shall  be  consecutively  tangent  to  each  other,  and  the  con- 
ditions that  these  arcs  shall  be  tangent  at  the  springing  lines 
and  the  crown  to  the  assumed  directions  of  the  tangents  to 
the  curve  at  those  points.  To  give  a  determinate  character  to 
fhe  problem,  there  must  be  imposed,  in  each  particular  case, 
certain  other  conditions  upon  which  the  solution  will  depend. 

When  the  tangents  to  the  curve  at  the  springing  lines  and 
•srown  are  respectively  perpendicular  to  the  span  and  rise,  the 
^urve  satisfying  the  above  general  conditions  will  belong  to 
Jie  class  of  oval  or  basket-handle  curves;  when  the  tangents 
it  the  springing  lines  are  perpendicular  to  the  span,  and  those 
it  the  crown  are  oblique  to  the  rise,  the  curves  will  belong  to 
the  class  of  pointed  or  obtuse  curves. 

The  pointed  curve  gives  rise  to  the  pointed  or  Gothic 
itch. 

If  the  intrados  is  to  be  an  oval  or  basket-handle,  and  its 


OVALS   O»   THREE   CENTRES. 


259 


rise  is  to  be  not  less  than  one-third  of  the  span,  the  oval  of 
three  centres  will  generally  give  a  curve  of  a  form  more  pleas- 
ing to  the  eye  than  will  one  of  a  greater  number  of  centres ; 
but  if  the  rise  is  to  be  less  than  a  third  of  the  span,  a  curve 
of  five,  seven,  or  a  greater  odd  number  of  centres  will  give 
the  more  satisfactory  solution.  In  the  pointed  and  obtuse 
curves,  the  number  of  centres  is  even,  and  is  usually  restricted 
to  four. 

353.  Three  centre  curves. — To  obtain  a  determinate 
solution  in  this  case  it  will  be  necessary  to  impose  one  more 
condition  which  shall  be  compatible  with  the  two  general 
ones  of  having  the  directions  of  the  tangents  at  the  springing 
lines  and  crown  fixed.  One  of  the  most  simple  conditions, 
and  one  admitting  of  a  great  variety  of  curves,  is  to  assume 
the  radius  of  the  curve  at  the  springing  lines.  In  order  that 
this  condition  shall  be  compatible  with  the  other  two,  the 
length  assumed  for  this  radius  must  lie  between  zero  and  the 
rise  of  the  arch ;  for  were  it  equal  to  zero  or  to  the  rise  there 
would  be  but  one  centre ;  and  if  taken  less  than  zero  or  greater 
than  the  rise,  then  the  curve  would  not  be  an  oval. 


FIG.  123. 

General  Construction.— Let  A  D  (Fig.  126)  be  the  half 
span,  and  A  C  the  rise.  Take  any  distance  less  than  A  C,  and  set 
it  off  from  D  to  R,  along  A  D ;  and  from  C  to  P,  along  A  C. 
Join  R  and  P,  bisect  by  a  perpendicular.  Prolong  this  per- 
pendicular until  it  intersects  C  A  produced.  Then  S,  R,  and 
a  point  on  A  B,  distant  from  A  equal  to  A  R,  will  be  the  three 
centres  of  the  required  oval. 

It  is  evident  that  there  will  be  an  infinite  number  of  ovala 
for  the  same  span  and  rise. 


260  CIVIL  ENGINEERING. 

For,  denote  by  R  the  radius  S  C  of  the  arc  at  the  crown, 
by  r  the  radius  R  D  at  the  springing  line,  by  a  the  half  span 
A  D,  and  by  I  the  rise  A  C. 

There  results  from  the  right  angled  triangle  S  A  R, 

SR2  =  ATS2  + A~R*, 
or 

(R  -  rf  =  (R  -  J)2  +  (a  -  r)*, 

from  which  is  obtained 

^  _  $  +  &8  _  2ar 
2(&  -  r)     ' 

which  may  be  satisfied  by  an  infinite  number  of  sets  of  values 
of  B.  and  r. 

354.  To  construct  an  oval  of  three  centres,  with  the 
condition  that  each  of  the  three  arcs  shall  be  of  60°. 

Let  B  D  be  the  span  and  A  C  the  rise  (Fig.  126).  With  the 
radius  A  B  describe  Bba  of  90° ;  set  off  on  it  Bb  =  60°  ;  draw 
the  lines  ab,  JB,  and  kb ;  from  C  draw  a  parallel  to  db,  and 
mark  its  intersection  c  with  £>B;  from  c  draw  a  parallel  to 
AZ>,  and  mark  its  intersections  N  and  0  with  A  B,  and  C  A  pro- 
longed. From  N,  with  the  radius  N  B,  describe  the  arc  Be; 
from  0,  with  the  radius  00,  describe  the  arc  Cc.  The  curve 
BcC  will  be  the  half  of  the  one  satisfying  the  given  condi- 
tions, and  N  and  0  two  of  the  centres. 

355.  To  construct  an  oval  of  three  centres  imposing  the 
condition  that  the  ratio  between  the  radii  of  the  arcs  at  the 
crown  and  springing  line  shall  be  a  minimum. 


Let  A  D  be  the  half  span,  A  C  the  rise  (Fig.  126).  Draw 
D  C,  and  from  C  set  off  on  it  Cd  =  Ca,  equal  to  the  differ- 
ence between  the  half  span  and  rise.  Bisect  the  distance  Dd 
by  a  perpendicular,  produced  until  it  intersects  C  A  prolonged. 
From  the  points  of  intersection,  R  and  S,  as  centres,  with  the 
radii  R  D  and  S  Q,  describe  the  arcs  D  Q  and  Q  C  ;  and  the 
curve  D  Q  C  will  be  the  half  of  the  one  required. 

For,  from  the  triangle  S  A  R,  we  get 

R      a2  -f  b*  -  2<w  , 

—  =  —  —  --  for  the  ratio. 

r          2b 


Differentiating  this  expression,  and  placing  its  first  differen- 


tial  coefficient  equal  to  zero,  -.  =  0,  there  results,  after  the 

ar 

terms  are  reduced, 


AH  OVAL   OF  FIVE  CENTRES. 


261 


r  = 


\ 


but  VV  +  #*  =  D  C,  and  Va2  +  V*  —  (a  —  1)  =  Dd,  hence  the 
given  construction. 

When  the  rise  is  less  than  one-third  of  the  span,  ovals  of 
three  centres  are  not  of  so  pleasing  a  shape,  and  one  of  five 
or  even  a  greater  number  of  odd  centres  must  be  used. 

356.  To  construct  an  oval  of  five  centres.— This  oval 
may  be  constructed  as  follows  (Fig.  127) : 


FIG.  127. 

Let  A  B  be  the  half  span,  and  A  C  the  rise  of  the  arch. 
Erect  at  B  a  perpendicular  to  A  B,  and  lay  off  B  D  equal  to 
A  C.  Join  B  and  C,  and  through  D  draw  D  0  perpendicular 
to  B  C,  and  produce  it  until  it  intersects  C  A  prolonged.  ^  Lay 
off  A  H  to  the  right  of  A  equal  to  A  C,  and  on  B  H  as  a  diame- 
ter describe  the  semicircle  B  E  H.  From  A  on  A  0  lay  off 
A  F  equal  to  C  E,  and  with  0  as  a  centre  and  F  0  as  a  radius 
describe  the  arc  F  N.  Lay  off  from  B,  on  B  A,  a  distance  B  L 


CIVIL   ENGINEERING. 


equal  to  AE,  and  with  R  as  a  centre  and  a  radius  equal  to 
R  L  describe  the  arc  L  N. 

The  points  0,  N,  and  R  are  the  centres,  and  0  Q,  N  M,  and 
R  B  =  R  M  are  the  radii  of  the  arcs  forming  the  oval. 

In  other  ways,  by  assuming  conditions  for  the  radii  of  the 
two  consecutive  arcs  from  the  springing  line,  other  ovals  of 
five  or  a  greater  number  may  be  constructed. 

The  curve  of  the  intrados  of  Perronriet's  fine  bridge  at 
Neuilly,  over  the  Seine,  is  an  oval  of  eleven  centres,  the 
radius  at  the  springing  line  being  21  feet,  and  at  the  crown 
159  feet,  the  span  being  128  feet,  and  the  rise  32  feet 

357.  Ovals  of  four  centres,  or  obtuse  and  pointed 
curves. — Their  constructions  are  analogous  to  those  already 
given  for  three  centres.  For  example — 

To  construct  an  oval  of  four  centres. — One  method  is 
as  follows : 

Let  A  B  (Fig.  128)  be  the  half  span,  A  C  the  rise  of  the 
required  curve  and  C  D  the  direction  of  the  tangent  to  it  at 


FIG.  128. 

the  crown.  At  C  draw  a  perpendicular  to  C  D.  Take  any 
point  R  on  A  B,  such  that  R  B  shall  be  less  than  the  perpen- 
dicular Rb  from  R  upon  the  tangent  C  D.  From  C,  on  the 
perpendicular  to  C  D,  set  off  Cd  equal  to  the  assumed  dis- 
tance R  B ;  draw  Rd  and  bisect  it  by  a  perpendicular,  which 
prolong  to  intersect  the  one  from  C  at  the  point  S  •  through 


TUDOR   ARCH. 


263 


S  and  R  draw  a  line ;  from  R,  with  the  radius  R  B,  describe 
an  arc,  which  prolong  to  Q  to  intersect  the  line  through  S  and 
R ;  from  S,  with  the  radius  S  Q,  describe  an  arc  which  will 
be  tangent  to  the  first  at  Q  and  pass  through  C.  The  curve 
B  Q  C  will  be  the  half  of  the  one  required  to  satisfy  the  given 
conditions. 

The  four- centred  Tudor  arch  is  generally  constructed  at 
follows : 

Let  A  B  (Fig.  129)  be  the  span,  and  divide  it  into  four  equ* 
parts,  the  points  of  division  being  D,  C,  and  D'. 


FIG.  129. 

From  D  and  D',  with  a  radius  equal  to  D  D',  describe  arw 
intersecting  at  E.  Through  E  draw  the  lines  D  E  and  D'E, 
and  produce  them  until  they  intersect  the  perpendiculars  to 
the  span  through  D  and  D'.  With  the  radius  D  A  describe 
the  arc  A  F,  and  with  the  radius  O'F  the  arc  F  H.  The  other 
half  is  drawn  in  a  similar  manner. 

358,  Voussoirs. — The  form  of  intrados  and  depth  of  key- 
stone being  determined,  the  form  of  the  extrados  and  the 
number  of  voussoirs  are  then  fixed.  The  shape  and  dimen- 
sions of  the  voussoirs  should  be  determined  both  by  geometri  • 
cal  drawings  and  numerical  calculation,  whenever  the  arch  is 
important,  or  presents  any  complication  of  form.  The  draw- 
ings should  be  made  to  a  scale  sufficiently  large  to  determine 
the  parts  with  accuracy,  and  from  these,  pattern  drawings 


264  CIVIL   ENGINEERING. 

may  be  constructed  giving  the  parts  in  their  true  size.  To 
mate  the  pattern  drawings,  the  side  of  a  vertical  wall  or  a  firm 
horizontal  area  ma)7  be  prepared  with  a  thin  coating  of  mor- 
tar, to  receive  a  thin,  smooth  coat  of  plaster  of  Paris.  The 
drawing  is  then  made  on  this  prepared  surface  by  construct- 
ing the  curve  by  points  from  its  calculated  abscissas  and  ordi- 
nates,  or,  where  it  is  formed  of  circular  arcs,  the  centres  fall- 
ing within  the  limits  of  the  prepared  surface,  by  using  the 
ordinary  instruments  for  describing  such  arcs.  To  construct 
the  intermediate  normals,  whenever  the  centres  of  the  arcs  do 
not  fall  on  the  surface,  an  arc  with  a  chord  of  about  one  foot 
may  be  set  off  each  side  of  the  point  through  which  the 
normal  is  to  be  drawn,  and  the  chord  of  the  whole  arc,  thus 
Bet  off,  be  bisected  by  a  perpendicular.  This  construction 
will  generally  give  a  sufficiently  accurate  practical  result  for 
elliptical  and  other  curves  if  of  a  large  size. 

From  the  pattern  drawings  thus  constructed,  templets  and 
bevels  are  made  which  guide  the  stone-cutter  in  shaping  the 
angles  and  surfaces  of  the  voussoirs. 

The  methods  of  representing  the  voussoirs  by  projections, 
and  from  them  deducing  the  true  dimensions  and  forms  of 
the  joints,  are  discussed  in  "  STONE  CUTTING." 

359.  Bond. — The  same  general  principles  are  followed  in 
arranging  the  joints  and  bond  of  the  masonry  of  arches,  as 
in  other  masonry  structures.  The  surfaces  of  the  joints 
should  be  normal  to  the  soffit,  and  the  surfaces  of  any  two 
systems  of  joints  should  be  normal  to  each  other  at  their  lines 
of  intersection.  These  conditions,  with  respect  to  the  joints, 
will  generally  be  satisfied  by  tracing  upon  the  soffit  its  lines 
of  least  and  greatest  curvature  and  taking  the  edges  of  one 
series  of  joints  to  correspond  with  one  of  these  systems  of 
lines,  and  the  edges  of  the  other  series  with  the  other  system, 
the  surfaces  of  the  joints  being  formed  by  the  surfaces  nor- 
mal to  the  soffit  along  the  respective  lines  in  question.  When- 
ever the  surface  of  the  soffit  is  a  single  curved  surface,  the 
joints  will  be  thus  either  plane  or  developable  surfaces. 

Hence,  in  the  right  cylindrical  arch  the  edges  of  one  series 
of  joints  will  correspond  to  the  right  line  elements  of  the 
cylindrical  surface,  while  those  of  the  other  will  correspond 
to  the  curves  of  right  section,  the  former  answering,  to  the 
line  of  least,  and  the  latter  of  greatest  curvature.  The  sur- 
faces of  the  joints  will  all  be  plane  surfaces,  and,  being 
normal  to  the  soffit  along  the  lines  in  question,  will  be  nor- 
mal also  to  each  other. 

In  full   centre  and  segmental  arches,  the  Tonssoirs  are 


OBLIQUE   ARCHES. 


265 


nsnally  made  of  the  same  breadth,  estimated  along  the  curve 
of  right  section.  In  the  right  cylindrical  arches  of  other 
forms  of  right  section,  it  may  not  in  many  cases  be  practi- 
cable to  give  to  all  the  voussoirs  the  same  breadth,  owing  to 
the  variable  curvature  of  the  right  section;  but  the  arrange- 
ment is  the  same  throughout  all  the  ring  courses. 

By  this  arrangement  of  the  joints  in  the  right  arch,  the 
joints  are  normal  to  each  other  and  the  coursing  joints  are 
very  nearly  perpendicular  to  the  pressure  they  have  to  sup- 
port. 

360.  Oblique  or  askew  arches. — When  the  obliqnityis 
considerable,  this  arrangement  of  the  coursing  joints  cannot 
be  used  for  the  oblique  arch,  as  the  pressure  would  be  very 
oblique  to  the  coursing  joints. 

The  best  method  for  the  coursing  joints  in  this  case,  when 
the  heading  joints  are  taken  parallel  to  the  face  of  the  arch, 
is  to  trace  curves  on  the  soffit  at  right  angles  to  the  edges  of 
the  heading  joints,  and  take  these  curves  as  the  edges  of  the 
coursing  joints  (Fig.  130).  The  projections  of  these  edges 
on  the  plane  of  the  springing  lines  are  logarithmic  curves, 
and  give  the  name  logarithmic  to  this  method. 


FIG.  130. — Elevation  and  plan  of  an  oblique  cylindrical  arch,  with  the 
edges  of  the  coursing  joints  constructed  by  the  logarithmic  method. 

The  logarithmic  method  makes  the  voussoirs  in  a  course 
variable  in  width,  and  gives  joints  difficult  to  execute. 

Another  method  is  much  used  in  preference,  by  which 
the  coursing  joints  are  kept  parallel  to  each  other.  This 
method,  known  as  the  helical  method,  consists  in  tracing 
on  the  soffit  for  the  edges  of  the  heading  joints,  helices  that 
are  parallel  to  the  helix  which  passes  through  the  extremi- 
ties of  the  span  and  rise  of  the  face  of  the  arch  (Fig.  131). 


266  CIVIL   ENGINEERING. 

Helices   are  then  drawn  on  the  soffit   perpendicular  to 
the  first  set  and  taken  for  the  edges  of  the  coursing  joints. 
The  logarithmic  and  helical  methods  are  used  for  arches 


FIG.   131. — Elevation  of  an  oblique  cylindrical  arcli  with  helical  joints. 

a,  voussoirs  of  cut  stone. 

c,  c,  bottom  course  of  stone  voussoirs  cut  to  receive  the  brick  courses. 

C,  face  of  the  abutment. 

D,  ends  of  the  abutments. 

of  considerable  obliquity.  "When  the  obliquity  is  slight,  the 
arch  may  be  built  of  separate  ribs,  each  rib  slightly  overlap- 
ping the  one  adjacent,  or  it  may  be  a  right  arch  supported 
on  piers  of  trapezoidal  cross-section. 


CONSTRUCTION  OF  ARCHES. 

Arches  may  be  either  of  stone,  brick,  or  mixed  masonry. 

361.  Arches  of  stone. — In  wide  spans,  and  particularly  in 
flat  arches,  cut  stone  alone  should  be  used. 

Rubble  stone  may  be  used  for  very  small  arches,  which  do 
not  sustain  much  weight,  or  as  a  filling  between  a  network  of 
the  ring  and  string  courses  of  larger  ones.  In  both  cases  the 
blocks  should  be  roughly  dressed  with  the  hammer,  and  the 
best  of  mortar  should  be  used. 

362.  Arches  of  brick. — Brick  may  be  used  alone  or  in 
combination  with  cut  stone  for  arches  of  considerable  size. 
The  brick  used  may  be  wedge-shaped,  or  of  the  common 
form.     There  is  no  difficulty  in  w^edge-shaped  bricks  accom- 
modating themselves  to  the  curved  shape  of  the  arch.     In 
common  brick  this  accommodation  can  be  partially  effect- 
ed by  making  the  joints  thicker  towards  the  extrados  than 
towards  the  intrados. 

Brick  arches  are  often  built  in  concentric  rings,  each  half 


ABCHES   OF 


MA8ONEY. 


267 


a  brick  thick,  the  connection  of  the  rings  depending  upon  the 
tenacity  of  the  mortar.  Continuous  joints  are  thus  formed 
parallel  to  the  soffit,  and  are  liable  to  vield  on  the  arch 
settling.  The  layers  are  called  shells.  This  method  should 
not  be  used  in  arches  of  more  than  thirty  feet  span.  Another 
mode  of  construction  is  to  lay  the  bricks  in  ordinary  string 
courses.  In  this  method  continuous  joints  are  formed,  ex- 
tending from  the  soffit  outward ;  they  are  necessarily  very 
open  at  the  back,  and  must  be  filled  with  mortar,  pieces  of 
slate,  or  other  material. 

To  obviate  the  defects  of  both  methods  as  much  as  possible, 
the  arch  may  be  constructed  by  building  partly  in  one  way 
and  partly  in  the  other ;  or,  as  it  is  termed,  in  shells  and 
blocks  (Fig.  132).  This  method  is  to  use  blocks  of  brick- 
work built  as  solidly  as  possible,  separated  at  short  intervals 
by  portions  of  concentric  rings.  The  bricks  in  the  blocks 


FIG.  132. 


should  be  moulded  or  rubbed  down  to  the  proper  form, 
especially  in  arches  of  importance.  Pieces  of  hoop-iron  laid 
in  the  joints  would  increase  the  strength  of  the  bond. 

363.  Arches  of  mixed  masonry. — When  a  combination 
of  brick  and  cut  stone  is  used,  the  ring  courses  of  the  heads, 
with  some  intermediate  ring  courses,  the  bottom  string 
courses,  the  key-stone  course,  and  a  few  intermediate  string 
courses,  are  made  of  cut  stone,  the  intermediate  spaces  being 
filled  with  brick  (Fig.  133). 

The  voussoirs  which  form  the  ring  course  of  the  heads  are 


268 


CIVIL   ENGINEERING. 


usually  terminated  by  plane  surfaces  at  the  top  and  on  the 
sides,  for  the  purpose  or  connecting  them  with  the  horizontal 


FIG.  133. 

courses  of  the  head  which  lie  above  and  on  each  side  of  the 
arch  (Figs.  134  and  135). 


FIG.  134. 


FIG.  135. 


This  connection  may  be  made  in  various  ways.  The  points 
to  be  observed  are  to  form  a  good  bond  between  the  voussoirs 
and  horizontal  courses,  and  to  give  a  pleasing  architectural 
effect. 

Sometimes  the  voussoir  is  so  cut  as' to  form  an  elbow-joint, 
as  shown  at  0,  0,  in  Fig.  134.  This  is  objectionable  both  on 
account  of  waste  of  material  in  the  cutting  and  from  the 
liability  of  the  stone  to  split  when  the  arch  settles. 

364.  Cappings. — "When  the  heads  of  the  arch  form  a  part 
of  the  exterior  of  a  structure,  as  when  they  are  the  faces  of  a 
wall  or  the  outer  portions  of  a  bridge,  then  the  top  surface 
of  the  voussoirs  of  the  ring  courses,  between  the  heads,  is 
usually  left  in  a  roughly  dressed  state  to  receive  the  courses 
of  masonry,  termed  the  capping,  which  rest  upon  the  arch 
between  the  walls  of  the  head.  Before  laying  the  capping, 
the  joints  of  the  voussoirs  on  the  back  of  the  arch  should  be 
carefully  examined,  and,  wherever  they  are  found  to  be  open 
from  the  settling  of  the  arch,  they  should  be  filled. 


ABUTMENTS   AND   P1EB8. 

The  capping  may  be  of  brick,  rubble,  or  concrete.  W  hen 
the  arches  are  exposed  to  filtration  of  rain-water,  as  in  bridges, 
casemates  of  fortifications,  etc.,  the  capping  should  be  made 
water-tight. 

The  difficulty  of  forming  water-tight  cappings  of  masonry 
has  led  engineers  to  try  a  covering  ol  asphalt  laid  upon  con- 
crete. This  asphalt  is  put  on  as  previously  described,  using 
sometimes  several  coats,  care  being  taken  to  make  the  squares 
of  each  successive  layer  break  joints  with  the  preceding. 

In  a  range  of  arches,  like  those  of  bridges  or  casemates, 
the  top  of  the  capping  of  each  arch  forms  two  inclined  sur- 
faces, like  those  ot  a  common  roof.  The  bottom  of  these 
surfaces,  by  their  junction,  form  gutters  where  the  water  col- 
lects, and  from  which  it  is  conveyed  off  in  conduits,  formed 
either  of  iron  pipes  or  of  openings  made  through  the  masonry 
of  the  piers. 

When  the  space  between  the  head  walls  above  the  capping 
is  filled  in  with  earth,  a  series  of  drains  should  be  made  run- 
ning from  the  top  or  ridge  of  the  capping,  and  leading  into 
the  main  gutter  drain.  They  are  made  of  dry  brick  laid  flat, 
with  intervals,  being  covered  by  other  courses  of  dry  brick 
with  open  joints. 

365.  Abutments  and  piers. — The  same  care  and  precau- 
tions  recommended    in  constructing  retaining  walls  apply 
equally  to  the  construction  of  abutments  and  piers. 

When  abutments,  as  in  the  case  of  buildings,  require  to  be 
of  considerable  height,  and  would  therefore  demand  extraor- 
dinary thickness  if  used  alone  to  sustain  the  thrust  of  the 
arch,  they  may  be  strengthened  by  carrying  them  up  above 
their  connection  with  the  arch,  thus  adding  to  their  weight, 
as  in  the  battlements  and  pinnacles  of  Gothic  architec- 
ture ;  by  adding  to  them  ordinary,  full,  or  arched  buttresses, 
termed  flying  buttresses ;  or  by  using  ties  of  iron  below 
the  key-stone  to  connect  the  voussoirs  which  are  near  the 
joints  of  rupture.  The  employment  of  these  different  expe- 
dients, their  forms  and  dimensions,  will  depend  on  the  char- 
acter of  the  structure  and  the  kind  of  arch.  The  iron  tie, 
for  example,  cannot  be  hidden  from  view  except  in  the  plate- 
band,  or  in  very  flat  segmental  arches ;  and  wherever  its  ap- 
pearance would  be  unsightly  some  other  expedient  must  bo 
tried. 

366.  Connection  of  the  arch  -with  its    abutment. — 
Care  should  be  taken  to  make  a  firm  connection  between  the 
lowest  courses  of  the  arch  and  the  top  of  the  abutment,  par- 
ticularly in  the  askew  and  segmental  arches. 


270  CIVIL   ENGINEERING. 

The  top  stone  of  the  abutment,  or  cushion  stone,  should  be 
well  bonded  with  the  stones  of  the  backing ;  should  be  made 
thick  enough  to  resist  the  pressure  brought  to  bear  on  it ;  and 
made  secure  against  any  sliding. 


Machinery  Used  in  Construction. 

367.  Scaffolding  and  hoisting  arrangements  are  necessary, 
and  are  in  all  things  similar  to  those  used  for  other  stone 
masonry.  In  addition,  strong  frames  called  centerings  are 
used.  From  the  nature  of  an  arch,  formed  as  it  is  of  separate 
pieces,  it  is  evident  that  it  could  not  be  placed  in  position 
without  some  artificial  support  for  the  blocks  to  rest  upon 
during  construction.  When  the  arch  is  completed  the  arti- 
ficial support  is  removed,  leaving  clear  the  space  arched  over. 
This  artificial  support  is  called  the  centre  or  centering  of 
the  arch,  and  is  made  generally  of  wood. 

A  centre  may  be  defined  to  be  a  wooden  frame  which 
supports  the  voussoirs  of  an  arch  while  the  latter  is  in  pro- 
gress of  construction. 

It  consists  of  a  number  of  vertical  frames,  termed  ribs, 
upon  which  horizontal  beams,  called  bolsters,  are  placed  to 
receive  the  voussoirs  of  the  arch.  These  ribs  are  placed 
from  five  to  six  feet  apart,  and  have  the  upper  or  bearing 
surface  curved  to  a  figure  parallel  to  that  of  the  soffit  of  the 
arch.  For  an  arch  of  considerable  weight,  the  pieces  form- 
ing the  back  of  the  centre  on  which  the  bolsters  rest  consist 
of  beams  of  suitable  lengths  shaped  to  the  proper  curvature 
and  abutting  end  to  end,  the  joints  between  them  being  nor- 
mal to  the  curved  surface.  The  joints  are  usually  secured  by 
short  pieces,  or  blocks,  placed  under  the  abutting  ends  and  to 
which  the  pieces  are  bolted.  The  blocks  are  shaped  so  as  to 
form  abutting  surfaces  for  struts  which  rest  against  them  and 
against  firm  points  of  support  beneath.  To  prevent  the  struts 
from  bending,  braces  or  bridle  pieces  are  used,  and  the 
whole  frame  is  firmly  connected  by  iron  bolts. 

This  is  the  general  construction  of  a  centre.  The  position 
of  the  points  of  support  and  the  size  of  the  arches  will  affect 
materially  the  combinations  of  the  parts. 

If  for  a  light  arch,  as  that  thrown  over  a  window  or  a 
door,  planks  instead  of  beams  are  used  to  form  the  back,  and 
two  ribs  only  are  required.  Their  construction  is  shown  in 
(Fig.  136). 


CONSTRUCTION   OF  CENTRES. 


271 


In  the  figure,  the  centre  is  shown  resting  on  the  walls.     If 
the  intrados  is  to  be  tangent  to  the  inner  face  of  the  wall*, 


1        1      1 

I.I.I.., 

1,1       1 

1        1        1 

A*"  "  ^^^xj 

L*~*±~r*~  SJ 

PIG.  136. 


supports  must  be  placed  next  to  the  wall,  as  shown  in  Fig. 
1J7,  to  hold  up  the  centre. 


FIG.  137. 

If  the  arch  be  heavier,  an  arrangement  puch  as  shown  in 
Pig.  137  may  be  used,  in  which  the  back  may  consist  of  two 
or  three  thicknesses  of  plank  nailed  together,  or  of  pieces  of 
scantling  of  proper  size. 

Tne  points  to  be  considered  in  the  construction  cf  centres 
are,  that  the  upper  or  bearing  surface  shall  be  correctly 
fort,  <ed ;  that  the  centre  shall  be  strong  enough  to  bear  the 


272 


CIVIL   ENGINEERING. 


load  which  is  to  be  placed  upon  it ;  that  is,  to  support  the 
weight  of  voussoirs,  workmen,  tools,  etc.,  without  sinking  or 
changing  its  form  during  the  construction  of  the  arch  ;  and 
that  it  may  be  easily  and  conveniently  removed  without  in- 
jury when  the  arch  is  completed. 

The  most  important  centerings  are  those  used  in  the  con- 
struction of  bridges  of  wide  span,  and  of  domes  of  important 
public  buildings. 

368.  General  remarks. — The  rules  given  for  laying  ash- 
lar or  cut-stone  masonry  should  especially  be  strictly  observed 
in  the  construction  of  arches.  The  manner  of  laying  the 
voussoirs  which  form  the  head  of  the  arch  demands  peculiar 
care.  The  arch  should  be  built  up  equally  and  simultane- 
ously on  the  two  sides  of  the  centering,  so  that  its  construc- 
tion should  not  be  more  rapid  on  one  side  than  on  the  other. 
The  load  on  the  centering  will  in  this  way  be  kept  sym- 
metrical. 

The  centres,  particularly  of  large  arches,  should  not  be  re- 
moved until  the  mortar  has  set;  it  is  recommended  that,  after 
removing  the  centre,  the  arch  should  be  allowed  to  settle  and 
assume  its  permanent  state  before  any  load  is  placed  upon  it. 


Fio.  138. 


Very  flat  arches  and  plate-bands  over  doorways  or  wide 
openings  in  a  wall  have  segmental  arches  placed  above  (Fig. 
138)  to  relieve  them  from  the  weight  of  the  wall  which 


GENERAL   PRINCIPLES.  273 

otherwise  would  rest  upon  them.  From  the  object  of  these 
additional  arches,  they  receive  the  name  or  relieving 
arches. 

The  principles  of  the  arch  should  be  thoroughly  under- 
stood by  the  engineer  as  well  as  the  architect. 

The  form  of  the  arch  will  depend  upon  the  purposes  which 
it  has  to  serve,  the  locality,  and  the  style  of  architecture 

The  full  centre  arch  is  the  strongest,  and  should  be  used 
when  great  strength  is  required  and  no  limit  to  the  rise  is 
imposed.  The  elliptical  is  regarded  as  the  most  graceful 
arch,  the  segmental  as  the  most  useful. 

Pointed  arches  are  used  in  buildings,  especially  those  of  the 
Gothic  order,  but  are  not  as  a  rule  used  for  bridges  or  similar 
structures. 

369.  Origin  and  use  of  the  arch. — It  is  a  matter  in  ques- 
tion, to  what  country  or  people  the  world  is  indebted  for  the 
arch.  But  there  is  no  doubt  that  Europe  is  indebted  to  the 
Romans  for  the  general  use  of  the  arch  in  building.  The  full 
centre  and  segmental  arches  especially  were  much  used  by 
them  in  the  construction  of  both  public  and  private  works,  as 
temples,  palaces,  private  residences,  baths,  sewers,  bridges, 
aqueducts,  etc.,  whose  remains  are  still  to  be  seen.  The 
Romans  were  the  first  to  use  the  dome  for  covering  temples. 

Afterwards,  the  arch  under  various  forms  became  an  essen- 
tial element  in  the  construction  of  buildings  throughout  Eu- 
rope. And  still  later  it  forms  in  the  United  States  a  promi- 
nent feature  of  all  our  constructions,  although  it  has  not  by 
us  been  used  to  the  same  extent  in  bridges  as  by  Europeans. 


GENERAL  RULES  TO  BE  OBSERVED  IN  THE  CONSTRUC- 
TION OF  MASONRY. 

370.  From  what  has  preceded,  the  following  general  rules 
may  be  stated  : 

1.  To  build  the  masonry  in  a  series  of  courses,  which  shall 
be  perpendicular,  or  as  nearly  so  as  practicable,  to  the  direc- 
tion of  the  force  which  they  have  to  resist. 

2.  To  avoid  the  use  of  continuous  joints  parallel  to  the 
direction  of  the  force. 

3.  To  use  the  largest  stones  in  the  lower  courses. 

4.  To  lay  the  lower  courses,  the  force  acting  vertically,  on 
their  natural  bed.     Where  great  strength  is  required  in  these 
courses,  the  beds  should  be  dressed  square. 

5.  To  moisten  all  dry  and  porous  stones  before  bedding 

18 


274:  CIVIL   ENGINEERING. 

them  in  mortar,  and  to  thoroughly  cleanse  from  dust,  etc.t 
their  lower  surfaces,  and  the  bed  of  the  course  on  which  the 
stones  are  to  be  laid. 

6.  To  reduce  the  space  between  each  stone  as  much  as  pos- 
sible, and  to  completely  fill  the  joint  with  mortar. 


PRESERVATION   OF   MASONRY. 

871.  Masonry  is  frequently  injured  by  the  mortar  being 
washed  out  of  the  joints  by  the  weather,  by  unequal  settling, 
or  by  the  expansion  and  contraction  of  the  material  due  to 
changes  of  temperature. 

372..  Pointing. — The  washing  out  of  the  mortar  from  the 
joints  may  be  prevented  by  means  of  pointing.  This  con- 
sists in  cutting  out  the  mortar  at  the  edge  of  the  joint  to  a 
depth  of  about  an  inch,  brushing  it  clean,  moistening  it,  and 
filling  it  with  pointing  mortar. 

The  pointing  mortar  is  made  of  cement  paste  and  clean, 
sharp  sand,  about  one  measure  of  paste  to  two  and  a  half  of 
sand  ;  or  if  mixed  dry,  one  of  cement  to  three  of  sand  by 
weight.  It  is  made  in  small  quantities  at  a  time,  the  in- 
gredients being  mixed  with  a  little  water,  and  thoroughly  in- 
corporated by  pounding  with  an  iron  pestle  in  an  iron  mortar. 

The  pointing  mortar  is  then  pressed  into  the  joint  and  its 
surface  rubbed  smooth  with  an  iron  tool.  The  practice  with 
the  United  States  engineers  is  to  calk  the  joints  with  a  ham- 
mer and  calking-iron  and  to  rub  the  surface  of  the  pointing 
with  a  steel  polishing  tool. 

To  obtain  a  good  pointing  is  quite  difficult,  as  the  unequal 
amount  of  contraction  and  expansion  of  the  stone  and  the 
pointing  mortar  causes  the  latter  to  crack,  or  to  separate 
from  the  stone.  Water  getting  into  the  cracks  and  freezing 
throws  out  the  pointing.  Some  builders  give  the  surface  of 
the  pointing  such  a  shape  that  the  water  shall  trickle  over 
the  pointing  without  entering  the  cracks  usually  found 
between  the  stone  and  the  pointing. 

The  period  at  which  pointing  should  be  done  is  not  fully 
agreed  upon  by  builders,  some  preferring  to  point  while  the 
mortar  in  the  joint  is  still  fresh,  or  green,  and  others  not 
until  it  has  become  hard.  The  latter  is  the  better  plan  ;  the 
former  is  the  cheaper,  as  the  joints  are  more  easily  cleaned  out. 

The  term  flash-pointing  is  sometimes  applied  to  a  thin 
coating  of  hydraulic  mortar,  made  with  a  large  proportion  of 
hydraulic  cement,  laid  over  the  face  or  back  of  a  wall  to  pro- 


PRESERVATION   OF   MASONRY.  275 

tect  the  joints  or  the  stone  itself  from  the  action  of  moisture 
and  the  weather. 

When  used  to  protect  the  stone,  the  sand  in  the  mortar 
should  be  coarse,  and  the  mortar  applied  in  a  single  uniform 
coat  over  the  surface,  which  should  be  thoroughly  cleansed 
from  dust  and  loose  mortar,  and  well  moistened  before  the 
application  is  made. 

373.  Precautions  against  unequal  settling. — A  certain 
amount  of  settling  always  takes  place  in  masonry,  due  to  the 
shrinkage  of  the  mortar  and  other  causes,  and  the  engineer 
must  take  every  precaution  to  ensure  that  this  settling  shall 
be  equal  throughout.     Otherwise,  especially  in  parts  sustain- 
ing unequal  loads,  and  which  are  required  to  be  firmly  joined 
together,  the  unequal  settling  that  takes  place  is  accompanied 
by  cracks  and  ruptures  in  the  masonry. 

To  avoid  this  unequal  settling,  it  is  advised  to  use  the  same 
thickness  of  mortar  throughout,  to  pay  particular  attention  to 
the  bond  and  correct  fitting  of  the  courses,  and  to  carry  up 
all  parts  of  the  wall  simultaneously.  If  the  walls  are  to  be 
subjected  to  heavy  vertical  pressures,  it  is  recommended  to 
take  the  further  precautions  of  using  hydraulic  instead  of 
common  mortar,  of  requiring  the  materials  to  be  uniform  in 
size  and  quality,  and  of  delaying  putting  the  permanent  load 
on  the  walls  until  the  season  after  the  masonry  is  laid.  It  is 
also  suggested  to  use  a  proof  load,  when  practicable,  before 
placing  on  the  permanent  one. 

374.  Effects  of  temperature  on  masonry. — Frost  is  the 
most  powerful  destructive  agent  against  which  the  engineer 
has  to  guard  in  masonry  constructions.     During  severe  winters 
in  the  northern  parts  of  our  country,  it  has  been  ascertained, 
by  observation,  that  the  frost  will  penetrate  earth  in  contact 
with  walls  to  a  depth  of  ten  feet;  it  therefore  becomes  a 
matter  of  the  first  importance  to  use  every  practicable  means 
to  drain  thoroughly  all  the  ground  in  contact  with  masonry 
to  whatever  depth  the  foundations  may  be  sunk  below  the  sur- 
face ;  for  if  this  precaution  be  not  taken,  accidents  of  the 
most  serious  nature  may  happen  to  the  foundations  from  the 
action  of  the  frost.     If  water  is  liable  to  collect  in  any  quan- 
tity in  the  earth  around  the  foundations,  it  may  be  necessary 
to  make  small  covered  drains  under  them  to  convey  it  off,  and 
to  place  a  stratum  of  loose  stone  between  the  sides  of  the 
foundations  and  the  surrounding  earth  to  give  the  water  a  free 
downward  passage. 

It  may  be  laid  down  as  a  maxim  in  building,  that  inortnr 
exposed  to  the  action  of  frost  before  setting  will  be  BO  much 


276  CIVIL  ENGINEERING. 

damaged  as  to  impair  materially  its  properties.  This  fact 
shows  the  necessity  of  using  hydraulic  mortar  to  a  height  of 
at  least  three  feet  above  the  ground  when  laying  foundations 
and  the  structure  resting  on  them ;  for  although  the  mortar 
of  the  foundations  might  be  protected  from  the  action  of  the 
frost  by  the  earth  around  them,  the  parts  immediately  above 
would  be  exposed,  and  would  attract  the  moisture  from  the 
ground,  so  that  the  mortar,  if  of  common  lime,  would  not  set 
in  time  to  prevent  the  action  of  the  frosts  of  winter. 

In  heavy  walls  the  mortar  in  the  interior  will  usually  be 
secure  against  the  action  of  the  frost,  and  masonry  of  this 
character  might  be  carried  on  until  freezing  weather  com- 
mences ;  but  in  all  important  works  it  will  be  the  safer  course 
to  suspend  the  construction  of  masonry  several  weeks  before 
the  ordinary  period  of  frost. 

During  the  heat  of  summer  the  mortar  is  apt  to  be  injured  by 
drying  too  rapidly.  To  prevent  this  the  stone  or  brick  should 
be  thoroughly  moistened  before  being  laid ;  and  afterwards, 
if  the  weather  is  very  hot,  the  masonry  should  be  kept  wet 
until  the  mortar  gives  indications  of  setting.  The  top  course 
should  always  be  well  moistened  by  the  workmen  when  quitting 
their  work  for  any  short  period  during  very  warm  weather. 

The  effects  produced  by  a  high  or  low  temperature  on  mor- 
tar in  a  green  state  are  similar.  In  the  one  case  the  freezing 
of  the  water  prevents  a  union  between  the  particles  of  the 
lime  and  sand  ;  and  in  the  other,  the  same  result  arises  from 
the  water  being  rapidly  evaporated.  In  both  cases  the  mortar 
is  weak  and  pulverulent  when  it  has  set. 

375.  Repairs  of  masonry. — In   repairing  masonry  it   is 
necessary  to  connect  the  new  work  with  the  old.     To  do  this, 
the  surface  of  the  old,  where  the  junction  is  to  be  made, 
should  be  arranged  in  steps  and  the  mortar  along  this  surface 
be  scraped  and  cleaned.     The  new  work  is  then  joined  to  the 
steps  by  a  suitable  .bond,  care  being  taken  to  have  the  surfaces 
fitted  accurately,  and  to  use  the  least  amount  of  mortar  that 
will  effect  the  required  object. 

MENSURATION   OF  MASONRY. 

376.  Engineers,  when  measuring  or  estimating  quantities 
of  masonry,  state  them  in  cubic  feet  or  yards.     Builders  and 
contractors  often  use  other  modes,  as  perches  of  stone,  rods  of 
brickwork,  etc.     To  avoid   misunderstanding,  the  engineer 
should  inform  himself  of  the  modes  used  in  the  locality  where 
his  work  is  to  be  milt. 


PART   V. 

FOUNDATIONS 


CHAPTER  XL 

377.  The  term,  foundation,  is  used  to  designate  the  lowest 
portion  or  base  of  any  structure. 

This  term  is  frequently  applied  to  that  portion  of  the  solid 
material  of  the  earth  upon  which  the  structure  rests,  and  also 
to  the  artificial  arrangements  which  may  be  made  to  support 
the  base. 

It  is  recommended  to  restrict  the  use  of  the  term,.founda 
tion,  to  the  lower  courses  of  the  structure,  and  to  use  the 
term,  bed  of  the  foundation,  when  either  of  the  other  two 
are  meant. 

378.  In  the  preceding  chapters,  the  foundations  of  the 
structures  there  considered  have  been  regarded  as  secure. 
Since  the  permanence  of  structures  depends  greatly  upon  the 
Bafety  of  the  foundations,  it  is  plain  that  the  importance 
attached  by  engineers  to  the  proper  construction   of  the 
latter  cannot  be  over-estimated. 

379.  Foundations  are  liable  to  yield  either  by  sliding  on 
their  beds  or  by  turning  over  by  rotation  about  one  of  the 
edges.     In  general,  if  care  is  taken  to  prevent  rotation,  there 
need  be  no  fear  of  yielding  by  sliding,  especially  if  the  bed  is 
a  hard  ground  or  other  compact  material. 

If  the  bed  is  of  a  homogeneous  material  and  the  pressure 
borne  by  the  foundations  is  uniformly  distributed  over  it, 
there  will  be  no  tendency  to  overturn,  and  the  settling,  which 
always  exists  to  a  greater  or  less  extent,  will  be  uniform 
throughout. 

If  the  material  forming  the  natural  bed  is  not  homogeneous, 
or  the  centre  of  pressure  does  not  coincide  with  the  centre  of 
figure  of  the  base,  unequal  settling  will  take  place,  followed 
by  cracks  and  ruptures  in  the  masonry,  and  finally,  undei 
certain  circumstances,  by  the  destruction  of  the  work. 


278  CIVIL   ENGINEERING. 

The  main  objects  to  be  attained,  in  preparing  the  bed  and 
foundation  of  any  structure,  are  to  reduce  the  settling  to  the 
smallest  possible  amount,  and  to  prevent  this  settling  from 
being  unequal. 

380.  The  beds  of  foundations  are  divided  into  two  classes : 

1.  Natural  beds,  or  those  prepared  in  soils  sufficiently 
firm  to  bear  the  weight  of  the  structure ;  and 

2.  Artificial  "beds,  or  those  which  require  an  artificial  ar- 
rangement to  be  made  to  support  the  structure,  in  consequence 
of  the  softness  or  want  of  homogeneousness  of  the  soil. 

Before  a  selection  of  the  kind  of  bed  can  be  made,  it  is 
necessary  to  know  the  nature  of  the  subsoil.  If  this  is  not 
already  known,  it  is  determined  ordinarily  by  digging  a 
trench  or  sinking  a  pit  close  to  the  site  of  the  proposed  work, 
to  a  depth  sufficient  to  allow  the  different  strata  to  be  seen. 
For  important  structures,  the  kind  of  subsoil  is  frequently 
made  known  by  boring  with  the  tools  usually  employed  for 
this  purpose. 

When  this  method  is  used,  the  different  kinds  and  thick- 
nesses of  the  strata  are  determined  by  examining  the  speci- 
mens brought  up  by  the  auger  used  in  boring. 

381.  Soils  are  divided,  with  reference  to  foundations,  into 
three  classes : 

1.  Those   composed  of   materials   whose   stability  is   not 
affected  by  saturation  with  water,  and  which  are  firm  enough 
to  support  the  weight  of  the  structure. 

2.  Those  firm  enough,  but  whose  stability  is  affected  by  the 
presence  of  water. 

3.  Compressible  or  soft  soils. 

Rock,  compact  stony  earths,  etc.,  are  examples  of  the  first 
class;  clay,  sand,  fine  gravel,  etc.,  are  examples  of  the  sec- 
ond; and  common  earth,  marshy  soils,  etc.,  are  examples  of 
the  third. 

The  beds  are  prepared  either  on  land  or  under  the  water. 


FOUNDATIONS  ON  LAND. 

There  will  be  three  cases,  corresponding  to  the  three  kinds 
of  soil  in  which  the  bed  is  to  be  prepared. 

1.     BEDS   PREPARED   IN   SOILS   OF   THE   FIRST   CLASS. 

382.  Rock. — When  rock  forms  the  material  in  which  the 
bed  is  to  be  made,  it  is  only  necessary  to  ascertain  if  the  rock 


FOUNDATIONS   ON   LAND.  279 

has  a  sufficient  area,  is  free  from  cavities,  and  sufficiently  thick 
to  support  the  structure  without  danger  of  breaking.  If  the 
rock  be  found  too  thin,  the  nature  of  the  soil  on  which  it 
rests  must  be  determined.  If  there  are  any  doubts  on  any 
of  these  points,  a  thorough  examination  into  the  thickness  of 
the  stratum  and  tests  upon  its  strength  should  be  made.  It 
is  also  recommended,  in  case  of  important  structures,  to  test 
further  its  strength  by  placing  on  it  a  trial  weight,  which 
should  be  at  least  twice  as  great  as  that  of  the  proposed 
structure. 

Having  become  satisfied  with  the  strength  of  the  rock,  all 
the  loose  and  decayed  portions  are  removed  and  the  surface 
levelled.  If  some  parts  are  required  to  be  at  a  lower  level 
than  others,  the  bed  should  be  broken  into  steps.  Fissures 
should  be  filled  with  concrete  or  rubble  masonry.  If  this 
filling  should  be  too  expensive,  arches  should  be  used.  In 
some  cases,  it  is  advisable  to  cover  the  whole  surface  of  the 
rock  with  a  layer  of  concrete. 

The  load  placed  on  the  rock  should  not  exceed  the  limit  of 
safety.  This  limit  is  taken  usually  at  one-tenth  of  the  load 
necessary  to  crush  the  rock. 

A  bed  in  solid  rock  is  unyielding,  and  appears  at  first  sight 
to  offer  all  the  advantages  of  a  secure  foundation.  It  is  found 
in  practice,  that  in  large  buildings  some  portions  will  not  rest 
on  the  rock,  but  on  some  adjacent  material,  as  clay  or  gravel. 
Irregularity  of  settlement  will  in  such  cases  almost  invariably 
follow,  and  give  great  trouble. 

383.  Compact  stony  earths,  etc. — The  bed  is  prepared 
in  soils  of  this  kind  by  digging  a  trench  deep  enough  to 
place  the  foundation  below  the  reach  of  the  disintegrating 
effects  of  frost.  A  depth  of  from  four  to  six  feet  will  gen- 
erally be  sufficient. 

The  bottom  of  the  trench  is  made  level,  both  transversely 
as  well  as  longitudinally,  and  if  parts  of  it  are  required  to  be 
at  different  levels,  it  is  broken  into  steps.  Care  should  be 
taken  to  keep  the  surface  water  out  of  the  trench,  and,  if 
necessary,  to  have  drains  made  at  the  bottom  to  carry  away 
the  water. 

The  weight,  resting  on  the  bottom  of  fhe  trench  should  be 
proportioned  to  the  resistance  of  the  material  forming  the 
bed.  The  limit  for  a  firm  soil  of  this  class  is  about  twenty- 
five  pounds  per  square  inch. 

It  is  usual,  in  order  to  distribute  the  pressure  arising  from 
the  weight  of  the  structure  over  a  greater  surface,  to  give 
additional  breadth  to  the  foundation  courses ;  this  increase 


280  CIVIL    ENGINEERING. 

of  breadtli  is  called  the  footing  or  spread.  In  compact 
soils,  the  spread  is  made  once  and  a  half  the  thickness  of  the 
wall,  and  in  ordinary  earth  or  sand,  twice  that  thickness. 


II.    BEDS   IN    SOILS    OF   THE    SECOND    CLASS. 

384  The  bed  is  prepared  in  a  soil  of  this  kind  by  digging 
a  trench,  as  in  the  previous  case,  deep  enough  to  place  the 
foundation  of  the  structure  bel  x*  the  injurious  effects  of 
frost.  Since  the  soil  is  effected  b}  saturation  with  water,  the 
ground  should  be  well  drained  before  the  work  is  begun,  and 
the  trenches  so  arranged  that  the  water  shall  not  remain  in 
them.  And  in  general,  the  less  a  soil  of  this  kind  is  exposed 
to  the  air  and  weather,  and  the  sooner  it  is  protected  from 
exposure,  the  better  for  the  work. 

In  this  case,  as  well  as  in  the  preceding,  it  was  supposed 
that  the  layer  of  loose  and  decayed  materials  resting  on  the 
soil  in  which  the  bed  is  to  be  prepared  was  of  moderate 
depth,  and  that  the  thickness  of  the  stratum  in  which  the  bed 
is  made  was  sufficient  to  support  the  weight  of  the  structure. 

It  sometimes  happens  that  this  firm  soil  in  which  the  bed 
is  to  be  made  rests  upon  another  which  is  compressible,  or 
which  is  liable  to  yield  laterally.  In  such  situations,  the 
weight  of  the  structure  should  be  reduced  to  its  minimum, 
and  should  be  distributed  over  a  bearing  surface  sufficiently 
large  to  keep  the  pressure  on  any  portion  of  the  bed  within 
certain  limits.  If  there  is  any  danger  from  lateral  yielding, 
the  bed  must  be  secured  by  confining  the  compressible  or 
yielding  soil  so  it  cannot  spread  out.  "This  may  be  done  by 
using  sheeting  piles,  or  other  suitable  contrivance. 


in.    BEDS   IN    SOILS    OF    THE    THIRD    CLASS. 

385.  In  soft  earths. — The  bed  is  prepared,  as  in  the  other 
cases,  by  digging  a  trench  sufficiently  deep  to  place  the  foun- 
dation courses  below  the  action  of  frost  and  rain. 

Greater  caution,  however,  must  be  observed  in  a  case  of 
this  kind  than  in  any  of  the  preceeding,  to  prevent  any  un- 
equal settling. 

The  bottom  of  the  trench  should  be  made  level  and  covered 
with  a  bed  of  stones,  sand,  or  concrete. 

If  stone  be  used,  it  is  the  practice  to  pave  the  bottom  of 
the  trench  with  rubble  or  cobble  stones,  which  are  well  set- 


BEDS   IN   SOFT   EARTHS. 


281 


tied  in  place  by  ramming,  and  on  this  paving  lay  a  bed  of 
concrete. 

If  sand  is  used,  the  sand  is  spread  in  layers  of  about  nine 
inches  in  thickness,  and  each  layer  well  rammed  before  the 
next  one  is  spread.  The  total  depth  of  sand  used  should  be 
sufficient  to  admit  of  the  pressure  on  the  upper  surface  of  the 
sand  being  distributed  over  the  entire  bottom  of  the  trench. 
(Fig.  139.) 


FIG.  139. 


FIG.  140. 


Another  method  of  using  sand  for  this  purpose  is  to  make 
holes  in  the  soil  or  in  the  bottom  of  the  trench  (Fig.  140),  and 
fill  them  with  moist,  well  packed  sand.  The  holes  are  about 
six  inches  in  diameter  and  five  or  six  feet  deep. 

Concrete  may  be  used  alone  in  the  trench,  or  spread  over  a 
layer  of  stones  well  rammed  in  place.  In  either  case,  the 
concrete  is  spread  in  layers  and  rammed  to  form  one  compact 
mass.  The  upper  surface  is  levelled  off,  and  the  foundation 
courses  begun  as  soon  as  the  concrete  has  set. 

A  concrete  bed  is  also  used  when  the  soil  is  all  sand  ;  a 
trench  is  dug  and  the  concrete  laid  as  just  described. 

The  pressure  allowed  on  a  concrete  bed  should  not  exceed 
one  tenth  part  of  its  resistance  to  crushing. 

By  distributing  the  weight  as  nearly  as  possible  uniformly 
over  the  foundation  courses,  the  dangers  of  unequal  settling 
may  be  avoided.  If  the  structure  rests  on  piers  or  other  sepa- 
rate supports,  these  supports  should  be  connected  by  inverted 
arches,  and  in  this  way  the  weight  is  distributed  over  the 
whole  bed.  If  the  weight  of  the  structure  varies  in  its  differ- 
ent parts  the  surfaces  of  the  bed  should  be  proportioned 
accordingly,  so  as  to  have  on  each  unit  of  surface  the  same 
amount  of  pressure 


282  CIVIL    ENGINEERING. 

386.  In  compressible  soil. — The  principal  difficulty  met 
with  in  forming  a  sufficiently  firm  bed  in  a  compressible  soil 
arises  from  the  nature  of  the  soil  and  its  yielding  in  all  direc- 
tions under  pressure.  There  are  several  methods  which  have 
been  used  successfully  in  soils  of  this  kind. 

One  method,  when  the  compressible  material  is  of  moder- 
ate depth,  is  to  excavate  until  a  firm  soil  is  reached,  and  then 
prepare  the  bed  as  described  in  the  previous  examples.  The 
great  objection  to  this  method  is  the  expense  of  excavation, 
especially  when  the  depth  of  excavation  is  considerable. 

A  second  method  is  to  drive  piles  through  the  soft  soil 
and  into  the  firm  soil  beneath  it.  The  piles  are  then  cut  off 
at  a  given  level,  fastened  firmly  together  by  heavy  timbers, 
and  a  platform  laid  upon  the  top  of  the  piles.  On  this  plat- 
form the  foundation  courses  of  the  structure  rest. 

A  third  is  to  use  a  modification  of  the  last  method.  In- 
stead of  the  piles  reaching  the  firm  soil,  they  are  only  driven 
in  the  compressible  one.  The  platform  is  made  to  extend 
over  so  large  an  area  that  the  pressure  on  the  unit  of  surface 
produced  by  the  weight  of  the  structure  is  less  than  the  limit 
allowed  for  this  particular  soil. 

A  fourth  is  also  a  modification  of  the  second  method,  and 
differs  from  the  last  one  in  using  piles  of  only  five  or  six 
inches  in  diameter  and  five  or  six  feet  long.  These  piles  are 
placed  as  close  together  as  they  can  be  driven,  and  support  a 
platform,  as  in  the  second  method.  The  object  of  the  short 
piles  is  to  compress  the  soil  and  make  it  firmer. 

A  fifth  is  to  enclose  the  area  to  be  covered  by  the  struc- 
ture by  sheet-piles.  The  piles  are  driven  to  the  firm  soil, 
but  not  necessarily  into  it.  The  enclosed  area  is  then  covered 
with  brush,  fascines,  or  other  similar  materials,  which  are 
pressed  down  into  the  soft  soil.  When  this  upper  layer  is 
sufficiently  firm,  the  foundation  is  begun. 

This  last  method  can  only  be  used  for  small  structures  of 
a  temporary  nature.  The  stability  of  the  construction  de- 
pends almost  entirely  upon  the  power  of  the  sheet-piles  to  re- 
sist the  pressure  transmitted  to  them  by  the  compressible  soil. 

In  general,  if  the  firm  stratum  beneath  the  compressible 
soil  can  be  reached  by  piles  of  ordinary  dimensions,  the 
second  method  is  the  one  preferred,  especially  in  those  situ- 
ations in  which  there  is  no  danger  of  the  piles  rotting. 

PILES. 
387.  A  pile  is  a  large  piece  of  iron  or  timber,  pointed  at 


PILES. 


one  end,  and  driven  or  forced  into  the  earth  to  be  used  gene- 
rally as  a  support  for  some  structure.  Piles  are  classified,  from 
the  'material  of  which  they  are  made,  into  wooden  and 
iron ;  from  their  length,  into  short  and  long  ;  from  the  form 
of  construction,  into  round,  square,  and  sheet-piles ;  an<J 
from  the  method  used  to  force  them  into  the  earth,  into  com- 
mon, screw,  and  pneumatic  piles. 

3S8.  Short  piles. — These  piles  are  usually  round,  from  six 
to  nine  inches  in  diameter,  and  from  six  to  twelve  feet  long, 
and  made  of  timber,  which  may  be  oak,  elm,  pine,  or  other 
suitable  wood,  the  particular  kind  depending  upon  the 
abundance  of  the  wood  in  the  vicinity  of  the  work  and  the 
particular  use  to  which  the  pile  is  to  be  placed.  Their  cross- 
section  is  sometimes  a  square.  Their  most  general  use  is 
to  compress  and  make  firmer  the  soil  in  which  they  are 
driven. 

389.  Long  piles. — These  are  either  round  or  square  in 
cross-section,  and  have  a  length  of  about  twenty  times  their 
mean  diameter  of  cross-section.  The  diameter  of  the  small 
end  should  not  be  less  than  nine  inches. 

They  are  generally  made  of  timber,  the  particular  kind 
depending  upon  circumstances  similar  to  those  given  for  the 
short  pile. 

The  long  wooden  pile  is  prepared  for  driving  by  having  all 
knots  and  rough  projections  trimmed  off,  and  having  the  end 
which  is  to  enter  the  earth  sharpened  to  a  point. 

This  point  should  be  kept  on  the  axis  of  the  pile,  and  the 
sharpening,  which  should  extend  for  a  distance  equal  to  once 
and  a  half  or  twice  the  diameter  should  also  be  symmetrical 
with  respect  to  the  same  line. 

If  the  ground  into  which  the  pile  is  to  be  forced  is  stony 
or  very  hard,  the  lower  extremity  of  the  pile  should  be  pro- 
tected by  an  iron  shoe.  The  shoe  should  be  pointed,  and  may 
be  made  of  cast  iron. 

The  head  of  the  pile  should  be  protected  from  the  blows 
used  to  force  it  down.  This  is  usually  effected  by  banding 
the  head  with  a  wrought-irou  hoop,  which  is  afterwards  re- 
moved. Major  Whistler's  plan  was  to  hollow  out  the  head  of 
the  pile  with  an  adze,  the  concavity  in  the  head  of  the  pile 
being  made  about  one  inch  deep,  and  then  to  cover  the  head 
of  the  pile  with  a  thin  piece  of  sheet  iron.  By  this  means 
the  piles  were  driven  without  injury.  t 

As  a  rule,  long  piles  are  used  to  support  a  weight  placed 
upon  them.  There  are  two  cases,  one  in  which  the  pile 
transmits  the  load  to  a  firm  soil,  thus  acting  as  a  pil  lar ;  the 


284  CIVIL   ENGINEERING. 

other  is  where  the  pile  and  the  load  are  wholly  supported  by 
the  friction  of  the  earth  on  the  sides  of  the  pile. 

390.  Sheet-piles. — These  are  flat  piles  of  rectangular  cross- 
section,  driven  side  by  side  in  a  vertical  position,  or  one  that 
is  nearly  so,  to  form  a  sheet.     The  use  of  this  sheet  is  either 
to  prevent  the  materials  enclosed  by  it  from  spreading  out, 
or  to  protect  them  from  the  undermining  action  of  water. 

Sheet-piles  are  prepared  for  driving  by  having  their  edges 
fitted,  so  as  to  ensure  a  close  contact.  *"  Sometimes  each  pile  is 
"  tongued  and  grooved,"  but  this  method  is  hardly  ever  neces- 
sary, for  if  the  sides  of  the  piles  in  contact  are  parallel  and 
the  piles  well  driven,  the  swelling  of  the  wood  by  the  water 
will  ensure  a  sufficiently  tight  joint. 

The  sheet-piles  are  kept  in  position  while  they  are  being 
driven  by  resting  them  against  horizontal  pieces  firmly  bolted 
to  guide-piles.  The  lower  end  of  the  sheet-pile  is  cut  with 
an  inclined  edge  for  the  purpose  of  giving  the  pile  a  drift 
towards  the  one  next  to  it. 

391.  Iron  piles. — Short,   long,   and    sheet-piles   are   fre- 
quently made  of  iron.    In  many  situations,  iron  piles  can  be 
used  to  advantage ;  it  is  not  probable,  however,  that  they  will 
ever  supersede  those  made  of  wood. 

The  long  iron  pile,  when  solid,  is  made  of  wrought  iron. 
The  best  form  for  those  of  cast  iron  is  tubular.  The  iron  pile 
is  forced  into  the  earth  either  by  means  of  a  screw  or  by  the 
pneumatic  process.  If  a  cast  iron  pile  is  to  be  forced  down 
by  blows  on  the  head,  a  wooden  punch  must  be  used  to  avoid 
the  danger  of  the  breaking  of  the  cast  iron  from  the  blows. 

Sheet-piles  of  cast  iron  have  been  frequently  used,  especially 
in  coffer-dams.  They  are  from  fifteen  inches  to  two  feet  wide, 
half  an  inch  thick,  and  generally  strengthened  by  flanges  or 
vertical  ribs.  The  joints  are  made  tight  by  making  each  pile 
overlap  the  two  adjacent  ones. 

The  difficulty  of  driving  iron  piles  so  that  all  their  heads  shall 
be  on  the  same  level  is  a  serious  objection  to  their  use  in  many 
cases.  This  objection  does  not  apply  to  their  use  in  a  coffer- 
dam, as  it  is  of  no  consequence  about  having  the  heads  of  the 
piles  on  the  same  level. 

392.  Screw  piles. — They  are  either  of  wood  or  iron.     Gen- 
erally they  are  made  of  iron.     The  screw  blade  is  ordinarily 
of  cast  iron,  fixed  on  the  foot  of  the  pile,  and  seldom  consists 
of  more  than  one  turn.     The  diameter  and  the  pitch  of  the 
screw  vary  with  the  nature  of  the  soil  and  the  load  to  be  sup- 
ported. 

The  piles  are  made  either  hollow  or  solid.     The  hollow 


PILES. 


285 


piles  are  of  cast  iron,  from  one  to  three  feet  in  diameter,  and 
generally  cast  in  convenient  lengths,  which  are  afterwards 
connected  together.  Fig.  141  shows  a  cast-iron  pile  of  the 
ordinary  kind  ;  it  is  about  two  feet  and  six  inches  in  diame- 
ter. Solid  piles  are  made  of  wrought  iron,  and  are  from  four 
to  nine  inches  in  diameter.  Fig.  142  shows  one  with  a  cast- 
iron  screw. 

Screw  piles  are  applicable  for  use  in  sand,  gravel,  clay,  soft 
rock,  and  alluvial  soils.  They  can  be  forced  into  very  hard 
soils,  even  into  brickwork.  To  force  them  into  the  earth,  it 
is  usual  to  fix  upon  the  top  of  the  pile  a  capstan,  and  to  apply 
the  power  to  the  levers  which  turn  it.  A  strong  frame-work 
is  needed  to  hold  the  pile  in  its  place  while  it  is  being  screwed 
down. 


FIG.  141. 


FIG.  142. 


FIG.  143. 


393.  Disk  piles.— These  are  hollow  iron  piles  with  the 
base  enlarged  by  a  broad  disk  attached  to  the  foot  (Fig. 
143),     They  have  been  used  successfully  in  light  sand. 

To  sink  them,  the  top  is  closed  except  where  a  tube  of 
small  diameter  is  inserted.  Through  this  small  tube,  water 
is  forced  at  high  pressure  by  a  force-pump,  and  as  the  water 
rushes  out  at  the  base  of  the  pile,  the  sand  is  disturbed  and  the 
pile  descends  by  its  own  weight.  When  it  has  descended  far 
enough,  the  pumps  are  stopped,  and  the  sand  settling  around 
the  pile  holds  it  firmly  in  position.  Great  caution  should  be 
observed  to  settle  the  foot  of  the  pile  some  distance  below  the 
scour,  or  that  point  where  there  is  danger  of  the  sand  being 
afterwards  disturbed  by  water  or  any  other  cause. 

394.  Pneumatic  piles. — These   are   iron  cylinders  often 
used  instead  of  common  piles  to  reach  a  firm  stratum  which 
lies  below  both  water  and  a  bed  of  soft  material,  as  in  the 
case  of  a  bottom  of  a  river. 

The  piles  are  sunk  through  this  soft  material  in  two  ways, 


286  CIVIL   ENGINEERING. 

either  by  exhausting  the  air  from  the  interior  of  the  cylinder, 
thus  producing  a  pressure  on  the  head  of  the  pile;  or  by 
forcing  air  into  the  tube,  thus  driving  the  water  out,  so  that 
workmen  are  able  to  descend  to  the  bottom  of  the  pile  and 
remove  any  obstructions  to  its  settling.  The  details  of  these 
methods  will  be  given  in  another  article. 

395.  Means  used  to  force  common  piles  into  the  earth. 
— Short,  long,  and  sheet-piles  of  wood  are  forced  into  the  earth 
most  generally  by  blows  delivered  on  the  heads  of  the  piles. 
The  machines  used  for  this  purpose  are  called  "  pile-drivers," 
and  are  of  various  kinds.     The  most  common  of  these  consists 
essentially  of  a  large  block  of  iron  which  slides  between  two 
uprights,  termed  guides  or  leaders.     This  block,  called  the 
ram  or  monkey,  having  been  drawn  to  the  top  of  the  guides, 
is  let  fall  and  comes  down  on  the  head  of  the  pile  with  a 
violent  blow,  forcing  the  pile  into  the  soil. 

The  pile-driver  may  be  worked  by  hand,  horse,  or  steam 
power. 

The  simplest  form  of  pile-driver  is  the  ringing  engine. 
In  this  machine  the  ram  is  attached  to  one  end  of  the  rope ; 
the  rope  passes  over  a  pulley,  and  its  other  end  branches 
out  into  a  number  of  smaller  ropes,  each  held  by  a  man. 
The  men,  all  pulling  together,  lift  the  ram  a  few  feet ;  then 
at  a  given  signal  all  let  go,  and  the  ram  falls  on  the  pile. 
The  number  of  men  required  will  depend  upon  the  weight  of 
the  ram.  It  is  usual  to  allow  about  forty  pounds  to  each 
man. 

In  the  machine  commonly  used,  the  ram  is  raised  by  the 
power  being  applied  to  a  windlass.  The  ram  is  held  while 
being  hoisted  by  tongs  or  nippers,  the  handles  of  which, 
when  the  ram  has  been  raised  to  the  proper  height,  come  in 
contact  with  two  inclined  planes  on  the  guides  ;  these  surfaces 
press  the  handles  of  the  tongs  together,  open  the  tongs  and 
let  the  ram  fall.  The  tongs  are  so  arranged  that  upon  being 
lowered  they  catch  hold  of  the  ram  by  a  staple  or  other  con- 
trivance on  its  upper  surface. 

If  the  piles  are  to  be  driven  in  an  inclined  position,  it  is 
only  necessary  to  incline  the  guides.  As  a  rule,  the  direc- 
tion of  the  pile  should  be  parallel  to  the  pressure  it  has  to 
support. 

396.  Other  machines  are  frequently  used  to  drive  piles. 
The  most  important  one  is  an  application  of  the  steam  ham- 
mer.    In  this  driver,  the  hammer  is  attached  to  a  piston-rod 
which  moves  in  a  cylinder  fixed  on  the  top  of  a  wrought-iron 
case  between  the  guides. 


PILE-DBTVTNG.  287 

The  steam  hammer  is  well  adapted  for  continuous  rows  of 
piles,  and  can  be  economically  used  where  there  are  a  great 
number  of  piles  to  be  driven,  and  where  they  are  near  each 
other. 

In  the  ordinary  pile-driver,  the  pile  is  driven  by  a  compara- 
tively small  mass  descending  from  a  considerable  height.  But 
with  the  steam  hammer,  the  pile  is  forced  into  the  earth  by 
the  rapid  blows  of  a  heavy  mass,  delivered  upon  a  block  weigh- 
ing several  tons,  placed  directly  over  the  head  of  the  pile.  The 
blows  are  given  at  the  rate  of  one  a  second,  and  the  hammer 
is  raised  each  time  only  to  a  height  equal  to  the  stroke  of  the 
piston. 

Various  methods  have  been  used  in  different  machines  for 
raising  the  ram.  In  some  cases  the  pressure  of  the  atmosphere 
has  been  tried  with  success.  In  one  machine  the  explosive 
properties  of  gunpowder  are  the  means  used. 

397.  If  the  head  of  a  pile  has  to  be  driven  below  the  level  to 
which  the  ram  descends,  another  pile,  termed  a  punch,  is  used 
for  the  purpose.  A  cast-iron  socket  of  a  suitable  form  embraces 
the  head  of  the  pile  and  the  foot  of  the  punch,  and  the  effect 
of  the  blow  is  thus  transmitted  through  the  punch  to  the.  pile. 

The  manner  of  driving  piles,  and  the  extent  to  which  they 
may  be  forced  into  the  subsoil,  will  depend  on  local  circum- 
stances. It  sometimes  happens  that  a  heavy  blow  will  effect 
less  than  several  lighter  blows,  and  that  piles,  after  an  inter- 
val between  successive  volleys  of  blows,  can  with  difficulty 
be  started.  Piles  may  be  driven  in  rocky  soils  and  even  in 
rock  itself,  if  holes  are  first  made  whose  diameters  are  a  little 
less  than  those  of  the  piles.  In  this  case  the  piles  should  be 
shod  with  an  iron  shoe.  Careful  attention  is  required  in  driv- 
ing, for  a  pile  has  been  known  to  break  below  the  surface 
and  to  continue  to  yield  under  the  blows  of  the  ram  by  the 
crushing  of  the  fibres  of  the  lower  end. 

The  test  of  a  pile  having  been  sufficiently  driven,  according 
to  the  best  authorities,  is  that  it  shall  not  sink  more  than 
one-fifth  of  an  inch  under  thirty  blows  of  a  ram  weighing  800 
pounds,  falling  five  feet  at  each  blow.  A  more  common  rule 
is  to  consider  the  pile  fully  driven  when  it  does  not  sink  more 
than  one-fourth  of  an  inch  at  the  last  blow  of  a  ram  weigh- 
ing 2,500  pounds,  falling  30  feet. 

The  least  distance  apart  at  which  piles  can  be  driven  with  ease 
is  about  two  aud  one-half  feet  between  their  centres.  If  the 
piles  are  nearer  than  this,  they  force  each  other  up  during  the 
driving.  The  average  distance  is  generally  about  three  feet. 

If  a  pile  has  to  be  drawn  out,  as  is  often  the  case,  a  lever 


238  CIVIL   ENGINEERING. 

fastened  by  a  chain  to  the  head  of  the  pile  may  be  used. 
Where  the  pile  is  only  partially  driven,  it  may  sometimes 
be  drawn  by  fastening  a  chain  around  the  head  of  the  pile 
and  attaching  it  to  the  nippers. 

398.  Load  on  piles. — Col.  Mason's  formula  is 

W-      E°     vA 

-B+^X5> 

in  which  W  is  the  greatest  load,  E  and  p  the  weight  re- 
spectively of  the  ram  and  pile,  all  in  pounds ;  h  the  fall  of 
the  ram,  and  d  the  penetration  of  the  pile  at  the  last  blow, 
both  in  feet.  He  used  a  factor  of  safety  of  4. 

T>  7 

Capt.  Sanders'  formula  is  W  =  -~  X  — ;  the  quantities  be- 
ing the  same  excepting  that  W  is  the  safe  load. 

The  rule  used  by  builders  is  to  limit  the  load  to  1,000 
pounds  on  the  square  inch  of  the  head  when  the  pile  trans- 
mits the  weight  to  firm  soil ;  and  to  200  pounds  when  it 
resists  by  friction  only. 

399.  Preparation  of  bed  in  compressible  soil,  using 
common  wooden  piles. — The  piles  having  been  driven  to 
the  firm  soil  beneath,  their  heads  are  sawed  off  at  a  given 
level  and  the  whole  system  is  firmly  connected  together  by 
longitudinal  and  cross  pieces  notched  into  each  other  and 
bolted  to  the  piles.     On  these  piles  a  platform  is  laid  ;  or  the 
soft  earth  around  the  top  of  the  piles  is  scooped  out  for  five 
or  six  feet  in  depth,  and  this  space  filled  with  concrete. 

If  a  platform  is  to  be  used,  it  is  constructed  as  follows : 
A  large  beam,  called  a  capping1,  is  first  placed  on  the  heads 
of  the  outside  rows  of  piles  and  is  fastened  to  them  by  iron 
bolts,  or  wooden  pins  termed  treenails.  Sometimes  an  occa- 
sional tenon  is  made  on  the  piles,  fitting  into  a  corresponding 
mortise  in  the  capping.  Other  beams  are  then  laid  resting 
on  the  heads  of  the  intermediate  piles,  with  their  extremities 
on  the  cappings,  and  are  then  bolted  firmly  to  the  piles 
and  cappings.  Another  set  of  beams  are  laid  at  right  angles 
to  these,  and  are  bolted  to  the  piles.  Where  the  beams  cross 
each  other,  they  are  both  notched  so  as  to  have  their  upper 
surfaces  in  the  same  plane.  The  beams  which  have  their 
lengths  in  the  direction  of  the  longer  sides  of  the  structure 
are  known  as  string  pieces,  and  the  other  set  are  termed 
cross  pieces. 

A  platform  of  thick  planks  is  laid  upon  the  upper  surface 
of  the  beams  and  is  spiked  to  them. 

The  cappings  are  sometimes  of  larger  size  than  the  other 
beams,  in  which  case  a  rabbet  is  made  in  the  inner  edge  so  as  to 
have  the  platform  flush  with  the  upper  surface  of  the  capping. 


GRILLAGE   AND   PLATFORM. 


289 


The  whole  construction  is  called  a  grillage  and.  platform. 
(Fig.  144.) 


—a  pIQ  144 — Represents  a  grillage 
and  platform  fitted  on  piles. 
A,  masonry, 
a,  a,  piles. 
6,  string  pieces. 

c,  cross  pieces. 

d,  capping  piece. 

e,  platform  of  plank. 
/,  concrete. 

<7,  soft  soil. 
?i.  firm  soil. 


400.  When  the  firm  stratum  into  which  the  piles  have  been 
driven  underlies  a  soil  so  soft  that  there  is  doubt  of  the  lateral 
stability  of  the  piles,  the  soft  soil  should  be  scooped  away  and 
stones  should  be  thrown  between  and  around  the  piles  to  in- 
crease their  stiffness  and  stability.  (Fig.  145.) 


FIG.  145 — Represents  the  manner  of 
using  loose  stone  to  sustain  piles  and 
prevent  them  from  yielding  laterally. 

A,  section  of  the  masonry. 

B,  loose  stone  thrown  around  the  piles. 


401.  If  the  situation  be  such  that  decay  in  the  timber  is  to 
be  expected,  the  more  costly  method  of  excavation  must  be 
adopted. 

The  practical  difficulty  met  when  trenching  in  such  cases,  is 
19 


290  CIVIL   ENGINEERING. 

the  presence  of  water  in  such  quantities  as  to  seriously  impede 
the  work,  even  to  the  extent  often  of  failure. 

Pumps  are  used  to  keep  the  water  out,  and  it  may  even  bo 
necessary  to  enclose  the  entire  area  by  a  sheet-piling.  In 
this  case,  two  rows  of  sheet-piles  are  driven  on  each  side  of 
the  space  to  be  enclosed,  through  the  soft  material  and  into 
the  firm  stratum  beneath.  The  soft  material  between  the  rows 
is  then  scooped  out,  and  its  place  filled  with  a  clay  puddling, 
forming  a  water-tight  dam  around  the  space  enclosed.  If  the 
water  comes  from  springs  beneath  the  dam  or  from  within 
the  area  enclosed,  this  method  will  fail,  and  it  may  be  neces- 
sary to  resort  to  some  of  the  methods  used  for  laying  founda- 
tions under  water. 


CHAPTER  XIL 

FOUNDATIONS   IN  WATER. 

402.  Two  practical  difficulties  meet  the  engineer  in  pre- 
paring beds  of  foundations  under  water.  One  is  to  make  the 
necessary  arrangements  to  enable  the  workmen  to  prepare 
the  bed ;  and  the  second,  having  prepared  the  bed,  to  secure 
it  against  the  deteriorating  effects  of  the  water  and  to  preserve 
its  stability. 

Preparation  of  the  bed. — The  situation  in  which  the  bed 
is  to  be  prepared  may  be  either  of  two  kinds  :  one  is  where  it 
may  be  prepared  without  excluding  the  water  from  the  place  ; 
and  the  other  is  where  the  water  must  be  excluded  from  tho 
area  to  be  occupied  before  the  bed  can  be  made. 


PREPARATION  OP   BED  WITHOUT  EXCLUDING  THE 
WATER. 

403.  Concrete  beds. — A  bed  of  concrete  is  frequently  used 
in  water.  To  prepare  the  bed,  the  upper  layer  of  loose,  soft 
soil  is  removed  by  a  dredging-machine  or  by  other  means,  and 
the  site  is  made  practically  level.  The  concrete  is  laid  within 
this  excavation.  A  conduit  made  of  wood  or  iron,  or  a  box 
or  contrivance  which  opens  at  the  bottom  when  jowered  in 
position,  may  be  used  in  laying  the  concrete. 


FOUNDATIONS   IN   WATER. 


291 


A  cylindrical  conduit  of  boiler  iron,  made  in  sections  of  suit- 
able lengths  which  can  be  successfully  fastened  on  or  detached 
as  the  case  requires,  has  been  used  with  success.  The  lower 
end  of  the  conduit  has  the  form  of  a  frustum  of  a  cone.  The 
whole  arrangement  is  lowered  or  raised  and  moved  about  at 
pleasure  by  means  of  a  crane.  The  concrete  is  placed  in  the 
conduit  at  the  upper  end,  and  by  a  proper  motion  of  the  crane 
is  spread  in  layers  as  it  escapes  from  the  lower  end.  By  lift- 
ing and  dropping  the  apparatus  the  layers  can  be  compressed. 

iBags  filled  with  concrete  have  been  used,  with  a  moderate 
degree  of  success,  for  the  same  purpose. 


a  a 

Section  on  A.B. 


FIG.  146. 


The  object  to  be  attained  is  to  get  the  concrete  placed  in 
fK>sition  in  as  nearly  as  possible  the  same  condition  as  when  it 


292  CIVIL  ENGINEERING. 

is  made.  If  it  be  allowed  to  fall  some  distance  through  water, 
or  be  placed  in  a  strong  current,  the  ingredients  of  the  con- 
crete are  liable  to  be  separated. 

Where  the  site  is  in  flowing  water,  it  is  often  necessary  to 
provide  some  arrangement  which,  by  enclosing  the  area  of  the 
site,  will  calm  the  water  within  the  enclosure,  and  will  thus  pre- 
vent its  inj  urious  effect  upon  the  fresh  concrete  before  it  has  set. 

404.  The  arrangement  shown  in  Figure  146  was  used  for  this 
purpose.     It  consisted  of  a  framework  composed  of  uprights 
connected  together  by  longitudinal  pieces  in  pairs ;  each  pair 
being  notched  on  and  bolted  to  the  uprights,  leaving  an  interval 
through  which  sheet-piles  were   inserted.       The   sheet-piles 
were  driven  into  close  contact  with  the  bottom,  which   was 
rock.     The  frame  was  put  together  on  the  shore  and  then 
floated  to  its  place.     It  was  secured  in  position  by  inserting 
the  uprights  in  holes  drilled  in  the  rock.      The   sheet-piles 
c,  c'j  were  then   inserted  between  the  horizontal  pieces  b,  £>', 
and   rested  on  the  bottom.      The  whole  area  was  thus  en- 
closed by  a  wooden  dam,  within  which  the  water  was  quiet. 
The  concrete  was  then  laid  on  the  bottom  of  the  enclosed 
space.     To  prevent  the  sides  of  the  dam  from  spreading  out 
iron  rods  d,  d,  d ,  d',  were  used  to  connect  them. 

405.  Beds  made  of  piles. — Common  wooden  piles  are  fre- 
quently used  to  form  a  bed  for  the  foundation  courses  of  a 
structure.      They  are  driven  through  the  soft  soil  into  the 
firm  stratum  beneath,  and  are  then  sawed  off  on  a  level  at  or 
near  the  bottom.     On  these  are  laid  a  grillage  and  platform 
or  other  suitable  arrangement  to   receive  the  lower  courses. 
Where  the  bottom  is  suitable  for  driving  piles,  and  there  is 
no  danger  of  scour  to  injure  their  stability,  this  method  is 
economical  and  efficient.     The  foundation  courses  must  be 
placed  in  position  by  some  submarine  process,  as  by  the  use 
of  a  diving-bell,  or  by  means  of  a  caisson. 

406.  Common  caisson. — This  caisson  (Fig.  147)  is  a  water- 
tight box,  whose  sides  are  ordinarily  vertical,  and  which  are  ca- 
pable of  being  detached  after  the  caisson  has  been  sunk  in  posi- 
tion.    The  bottom  of  the  caisson,  as  it  is  to  form  a  part  of  the 
foundation  of  the  structure,  is  made  of  heavy  timbers,  and 
conforms  in  its  construction  to  that  of  a  grillage  and  platform. 

The  size  of  the  timbers  for  the  bottom  is  determined  by  the 
weight  of  the  structure  which  is  to  rest  on  them,  and  for  the 
sides,  upon  the  amount  of  pressure  from  the  water  when  the 
caisson  rests  on  its  bed. 

The  sides  are  generally  made  of  scantling,  covered  with 
thick  plank.  The  lower  ends  of  the  scantling  or  uprights  fit 


CAISSONS. 


293 


into  shallow  mortises  made  in  the  cap  pieces  of  the  grillage. 
Beams  are  laid  across  the  top  of  the  caisson,  notched  upon  the 
sides  and  projecting  beyond  them.  These  cross  pieces  are 
connected  with  the  lower  beams  of  the  grillage  by  long  iron 
bolts,  which  have  a  hook  and  eye  joint  at  the  lower  end  and  a 
nut  and  screw  at  the  upper.  After  the  bolts  are  unscrewed 
at  the  top,  they  can  be  unhooked  at  the  bottom,  the  cross 
beams  raised,  and  the  sides  of  the  caisson  detached. 


PIG.  147 — Represents  a  cross- 
section  and  interior  end 
view  of  a  caisson.  The 
boards  are  let  into  grooves 
in  the  vertical  pieces  in- 
stead of  being  nailed  to 
them  on  the  exterior. 

a,  bottom  beams  let  into 
grooves  in  the  capping. 

6,  square  uprights  to  sustain 
the  boards. 

c,  cross  pieces  resting  on  b. 

d,  iron  rods  fitted  to  hooks  at 
bottom  and  nuts  at  top. 

e,  longitudinal  beams  to  stay 
the  cross  pieces  c. 

A,  section  of  the  masonry. 

B,  bed  made  01  piles. 
/,  guide  piles. 


In  a  caisson  which  was  used  in  building  a  bridge  pier,  the 
exterior  dimensions  of  the  principal  parts  were  nearly  as  fol- 
lows : 

The  caisson  was  63  feet  long,  21  feet  wide,  and  15  feet 
deep.  The  cross  beams  on  top  were  made  10  inches  square 
in  cross-section,  and  were  placed  about  three  feet  apart ;  the 
uprights  were  of  the  same  size  as  the  cross  pieces,  and  were 
placed  about  six  feet  apart. 

Much  larger  caissons  have  been  used,  especially  in  some  of 
the  engineering  constructions  in  England. 

The  caisson  is  built  at  some  convenient  place  where  it  can 
be  launched  and  towed  to  the  position  it  has  to  occupy.  The 
bed  having  been  prepared  by  levelling  off  the  bottom  or  by 
driving  piles,  the  caisson  is  floated  to  and  moored  over  the 
spot.  The  masonry  courses  are  then  laid  on  the  bottom  of 
the  caisson,  and  are  built  up  until  the  caisson  rests  on  its  bed. 
Just  before  it  reaches  the  bed,  it  is  sometimes  settled  in  place, 


294:  CIVIL   ENGINEEEING. 

by  admitting  water  into  the  interior,  and  an  examination 
made  as  to  its  proper  position.  If  it  does  not  occupy  its 
proper  place,  and  there  is  a  desire  to  change  the  position  of 
the  caisson,  the  gates  by  which  the  water  was  admitted  are 
Bhiit  and  the  water  is  pumped  out.  The  removal  of  the  water 
will  allow  it  to  float  and  a  rectification  of  its  position  may 
then  be  effected. 

The  caisson  having  been  satisfactorily  settled  in  position, 
the  masonry  is  built  above  the  surface  of  the  water,  and  the 
sides  are  then  detached  and  removed. 

Caissons  are  frequently  used  whose  sides  are  not  detached. 
This  is  especially  the  case  where  the  sides  are  of  a  permanent 
character.  These  might  be  termed  permanent  caissons. 

407.  Permanent  caissons. — Caissons    built    with    brick 
sides  and  timber  bottoms  were  used  to  construct  the  sea-wall 
at  Sheerness,  in  England,  in  1811-12.     After  being  sunk,  they 
were  filled  with  concrete. 

Rankine  mentions  a  kind  that  are  built  wholly  of  bricks 
and  cement,  arid  which  are  filled  with  concrete  after  being 
sunk  in  place. 

408.  Diving-apparatus. — The  bed  may  be  prepared  as  on 
dry  land,  provided  some  apparatus  be  used  which  will  admit 
of  the  workmen  executing  their  labors  notwithstanding  the 
presence  of  the  water.     Submarine  or  diving  armor  and  diving- 
bells  are  devices  which  are  frequently  used  for  this  purpose. 

I.  Submarine  armor. — This  is  an  apparatus  to  be  used  by 
a  single  person,  and  consists  essentially  of  a  metallic  helmet 
from  which  the  water  is  excluded  by  atmospheric  pressure. 
The  helmet  encloses  the  man's  head ;  rests  upon  his  shoulders 
and  is  connected  with  an  air  and  water-tight  dress  which  he 
wears.     He  is  supplied  with  fresh  air  forced  through  a  flexible 
tube  entering  at  the  back  of  the  helmet ;  a  valve  opening  out- 
wards allows  the  foul  air  to  escape.     To  enable  him  to  see, 
the  helmet  is  provided  with  eye-holes  protected  by  strong  glass. 

II.  Diving-bell. — The  form  of  diving-bell,  commonly  used, 
is  that  of  a  rectangular  box  with  rounded  corners.     Holes 
protected  by  strong  glass  about  two  inches  thick  are  made  in 
the  top  to  admit  light  into  the  interior.     Fresh,  air  is  forced 
through  a  flexible  tube  into  the  bell  by  means  of  air-pumps. 
The  bell  is  raised  and  lowered  by  means  of  a  crane  and 
windlass. 

A  bell,  whose  dimensions  are  four  feet  wide,  six  feet  long, 
and  five  feet  high  on  the  inside,  is  of  convenient  size  for  lay- 
ing masonry  under  water. 

ihe  diving-bell  has  been  much  used  in  laying  submarine 


WELL  FOUNDATIONS.  295 

foundations  where  there  was  no  scour  and  where  the  bed  was 
easily  prepared. 

409.  Pierre  perdue.— The  methods  just  given  are  appli- 
cable to  structures  of  moderate  dimensions,  but  when  the  area 
occupied  by  the  bed  is  very  considerable,  these  methods  are 
either  inapplicable  or  require  modifications.     One  known  by 
the  French  as  pierre  perdue  has  been  frequently  used.     It 
consists  in  forming  an  artificial  island  of  masses  of  loose  stone 
thrown  into  the  water,  and  allowing  the  stone  to  arrange  them- 
selves.    This  island  is  carried  up  several  feet  above  the  sur- 
face of  the  water  and  the  foundations  are  built  upon  it. 

The  structure  should  not  be  commenced  until  the  bed  has 
fully  settled.  If  there  is  any  doubt  about  this,  the  bed  should 
be  loaded  with  a  trial  weight,  at  least  twice  as  great  as  that  of 
the  proposed  structure. 

This  method  can  not  be  used  in  navigable  rivers  or  other 
situations  where  it  is  of  greater  importance  not  to  contract 
the  water-way. 

410.  Screw  piles. — Iron  screw  piles  have  been  used  with 
success  foT  foundations  in  localities  where  the  methods  already 
mentioned  were  not  practicable.     They  do  not  differ,  in  prin- 
ciple, from  the  common  wooden  pile.     Iron  piles  last  well 
both  in  fresh  and  salt  water ;  whereas  wooden  piles  can  not 
be  relied  upon  at  all  in  salt  water,  and  they  will  not  last  in 
fresh  water  unless  entirely  submerged. 

Iron  screw  piles  have  been  much  used,  in  the  United  States, 
in  the  construction  of  light-houses  on  or  near  sandspits  at  the 
entrance  of  our  harbors  and  on  shoal  spots  off  the  coast,  where 
it  would  be  almost  impossible  to  prepare  the  beds  by  any  of 
the  other  more  usual  methods. 

411.  Well  foundations. — In  India,  a  method  known  as 
well  or  block  foundations  has  been  quite  extensively  used, 
especially  in  deep  sandy  soils.     The  method  consists  in  sink- 
ing a   number  of  wells   close  together,   filling  them   with 
masonry,  and  connecting  them  together  at  top. 

The  method  of  sinking  one  of  these  wells  is  to  construct  a 
wooden  curb  about  a  foot  in  thickness ;  its  cross-section 
being  the  same  as  that  of  the  well,  and  to  place  it  in  position 
on  the  proposed  site.  On  this  curb  a  cylinder  of  brickwork 
is  built  to  a  height  of  about  four  feet.  As  soon  as  the  mortar 
has  set,  the  sand  is  scooped  out  from  under  the  curb,  and  it 
descends,  carrying  with  it  the  masonry.  When  the  curb  has 
settled  about  four  feet,  another  block  or  height  of  masonry  is 
added,  and  again  the  sand  is  scooped  out  from  under  the 
curb,  and  the  whole  mass  descends  as  before.  This  process 


296  CIVIL  ENGINEERING. 

is  then  repeated  and  carried  on  until  the  curb  has  reached  the 
required  depth.  Care  must  be  taken  to  regulate  the  excava- 
tion so  that  the  cylinder  shall  sink  vertically. 

From  the  very  nature  of  the  soil,  water  is  soon  met.  As 
long  as  the  water  can  be  kept  out  either  by  bailing  or  by 
pumping,  the  work  proceeds  with  rapidity.  If  the  water 
comes  in  so  fast  that  it  cannot  be  exhausted  by  these  means, 
the  sand  must  be  scooped  out  by  means  of  divers  or  by  some 
other  method.  Under  these  circumstances  the  excavation 
proceeds  slowly  and  with  difficulty. 

When  the  curb  reaches  a  firm  stratum,  or  a  depth  where 
there  is  no  danger  of  the  foundations  being  affected  by  the 
water,  the  bottom  is  levelled,  a  concrete  bed  made,  and  the 
interior  of  the  cylinder  filled  in  solid  with  masonry.  If  the 
concrete  bed  is  made  without  exhausting  the  water,  the  latter 
is  pumped  out  as  soon  as  the  concrete  sets,  and  the  masonry 
is  then  built  in  the  usual  manner. 

Cylinders  of  boiler  iron  have  been  used  in  the  same  way  as 
the  masonry  curbs,  and  are  an  improvement  upon  them. 

412.  Iron  tubular  foundations. — This  is  a  general  name 
applied  to  large  iron  cylinders  which  are  sunk  through  water 
and  a  soft  bottom  to  a  firm  soil,  and  used  to  support  a  given 
structure  in  the  same  manner  as  common  piles.  The  number 
and  size  of  the  tubes  depend  upon  the  weight  to  be  supported 
and  the  means  adopted  to  sink  them. 

The  method  just  described  for  the  well  is  frequently  used 
for  the  iron  tubes.  Brunei,  the  English  engineer,  in  building 
the  Windsor  Bridge,  on  the  Windsor  branch  of  the  Great 
Western  Railway,  employed  this  method  in  constructing  the 
abutments  of  the  bridge.  There  were  in  each  abutment  six 
cast-iron  cylinders,  each  six  feet  in  diameter,  and  they  were 
sunk  to  the  proper  depth  by  excavating  the  earth  and  gravel 
for  the  interior  with  dredges  and  by  forcing  the  cylinders 
down  by  weights  placed  on  the  top  of  each  one. 

The  concrete  bed  in  the  bottom  was  made  by  lowering  the 
concrete  in  bags,  which  were  arranged  so  that  by  pulling  a 
rope  the  bags  were  emptied  under  the  water  in  the  proper 
place.  When  a  sufficient  quantity  had  been  put  in  and  had 
hardened,  the  water  was  pumped  out  and  the  cylinders  filled 
in  the  usual  manner. 

This  method  does  not  differ  in  principle  from  a  foundation 
on  piles,  and  the  same  general  rules  apply  as  to  the  amount  of 
load  to  be  supported  and  the  depth  to  which  the  pile  is  to  be 
driven. 

In  some  cases  a  clump  of  common  piles  was  driven  within 


COFFER-DAMS.  297 

the  cylinder  at  the  bottom,  and  the  spaces  filled  with  concrete. 
In  some  of  the  recent  constructions  the  piles  extend  to  the  top 
of  the  cylinder. 


PREPARATION  OF  BED,  THE  WATER  BEING  EXCLUDED. 

413.  There  are  two  cases :  where  the  water  is  excluded  by 
means  of  a  dam,  and  where  it  is  excluded  by  atmospheric 
pressure. 

I.   EXCLUSION   OF   WATER  BY  DAMS. 

The  dams  used  are  the  common  earthen  or  clay  dam,  the 
common  coffer-dam,  and  modified  forms  of  the  coffer-dam. 

414.  Earthen  dam. — In   still  water  not   more  than  four 
feet  deep,  a  dam  made  of  earth  or  ordinary  clay  is  usually 
adopted  to  enclose  the  given  area  and  to  keep  out  the  sur- 
rounding water.     This  dam  is  made  by  digging  a  trench 
around  the  area  to  be  enclosed  and  removing  the  soft  material 
taken  out ;  the  earth  or  clay  is  then  dumped  along  the  line  of 
this  trench  until  it  rises  one  or  two  feet  above  the  surface  of 
the  water  ;  as  the  earth  is  dumped  in  place  it  should  be  firmly 
pressed  down,  and  when  practicable,  rammed  in  layers.     Any 
good  binding  earth  or  loam  will  be  a  suitable  material  for  the 
dam. 

The  dam  being  finished,  the  water  within  the  enclosed  area 
is  pumped  out,  and  the  bed  and  foundations  constructed  as 
already  prescribed  for  those  "  on  land." 

415.  Coffer-dam. — Where  the  water  is  more  than  four  feet 
deep,  and  especially  if  in  running  water,  the  common  earthen 
dam  would  be  generally  too  expensive  a  structure,  even  if  it 
could  be  built.     In  a  case  of  this  kind,  and  where  the  water 
does  not  exceed  twenty-five  feet  in  depth,  the  common  coffer- 
dam is  usually  employed. 

The  common  coffer-dam  (Fig.  148)  is  essentially  a  clay 
dam,  whose  sides  are  vertical  and  retained  in  position  by  two 
rows  of  piling. 

The  common  method  of  constructing  the  coffer-dam  is  to 
drive  two  parallel  rows  of  common  piles  around  the  area  to 
be  enclosed ;  the  distance  between  the  rows  being  equal  to 
the  required  thickness  of  the  dam,  and  the  piles  in  each  row 
being  placed  from  four  to  six  feet  apart. 

The  piles  of  each  row  are  then  connected  by  horizontal 


298 


CTVTL   ENGINEERING. 


beams,  called  string  or  wale  pieces,  which  are  notched  on 
and  bolted  to  the  piles  on  the  outside  of  each  row,  about  one 
foot  above  the  highest  water  mark.  On  the  inside  of  the 
rows,  and  nearly  opposite  to  the  wale  pieces,  are  placed  string 
pieces  of  about  half  the  size,  to  serve  as  guides 
to  the  sheet-piles. 


K"^  ^48-Representa 
A  section  of  a 
coffer-dam. 

a,  common  piles. 

5,  wale  or  string 
pieces. 

c,  cross  pieces. 

d,  sheet  piles. 

A,  puddling. 

B,  mud     and    loose 
soil. 

C,  firm  soil. 


The  two  rows  of  piles  are  tied  together  by  cross  pieces 
notched  on  and  bolted  to  the  outer  wale  pieces.  Upon  these 
CIVBS  pieces  are  laid  planks  to  form  a  scaffolding  for  the 
workmen  and  their  tools,  etc. 

The  sheet-piles  are  driven  in  juxtaposition  through  the  soft 
soil  and  in  contact  with  the  firm  soil  beneath.  They  are 
about  four  inches  thick  and  nine  inches  wide,  and  are  spiked 
to  the  inner  string  pieces.  Sometimes  an  additional  piece 
known  as  a  ribbon  piece,  is  spiked  over  the  sheet-piles. 

These  rows  of  sheet-piles  form  a  coffer  for  the  puddling 
whence  the  name  of  the  construction.  The  sheet-piles  having 
been  driven  and  secured  to  the  string  pieces,  the  mud  ancj 
soft  material  between  the  rows  are  scooped  or  dredged  out. 

The  puddling  which  forms  the  dam  is  then  thrown  in  and 
pressed  compactly  in  place,  care  being  taken  to  disturb  the 
water  as  little  as  possible  during  the  operation.  When  the 
top  of  the  puddling  rises  to  its  required  height,  pumps  are 
used  to  exhaust  the  water  from  the  enclosed  area.  The  in- 
terior  space  being  free  from  water,  the  bed  of  the  foundation 
is  prepared  as  on  dry  land . 

The   puddling  is  composed  of  clay  mixed  with  sand  or 


COFFEE-DAMS. 

gravel,  or  of  fine  gravel  alone,  freed  from  all  large  stones, 
roots,  or  foreign  material  which  may  be  mixed  with  it.  The 
clay  is  worked  into  a  plastic  condition  with  a  moderate 
amount  of  water,  and  then  mixed  thoroughly  with  a  given 
quantity  of  sand  or  fine  gravel.  Care  is  taken  that  there  are 
no  lumps  in  the  puddling  after  the  mixing. 

The  dam  is  given  the  required  strength  ordinarily  by 
making  the  thickness  equal  to  the  height  of  the  dam  above 
the  ground  or  bottom  011  which  it  is  to  rest,  when  this 
height  does  not  exceed  ten  feet.  For  greater  heights  the 
thickness  is  increased  one  foot  for  every  additional  height  of 
three  feet. 

This  rule  gives  a  greater  thickness  than  is  necessary  to  make 
the  dam  water-tight,  but  adds  to  its  stability.  The  stability 
of  the  dam  is  sometimes  still  further  increased  by  supporting 
the  sides  of  the  dam  by  inclined  struts,  the  upper  ends  of 
which  abut  against  the  inner  row  of  common  piles,  and  the 
lower  ends  against  piles  driven  for  that  purpose  into  the 
ground. 

416.  The  principal  difficulties  met  with  in  constructing  a 
coffer-dam  are  as  follows : 

First,  To  obtain  a  firm  hold  for  the  common  piles ;  a  dif- 
ficult thing  to  do  in  deep  muddy  or  rocky  bottoms ; 

Second,  To  prevent  leakage  between  the  surface  of  the 
ground  and  the  bottom  of  the  puddling ; 

Third.  To  prevent  leakage  through  the  puddling ; 

Fourth,  To  exhaust  the  water  from  the  enclosed  area  after 
the  dam  is  finished. 

These  difficulties  and  the  expense  of  construction  of  the 
dam,  increase  very  greatly  with  the  depth  of  the  water.  In 
deep  water,  the  size  and  length  of  the  piles  and  the  amount 
of  bracing  required  to  resist  the  pressure  of  the  water  render 
the  expense  very  great. 

Common  piles  can  not  be  efficiently  used  where  the  bottom 
is  rocky.  In  a  case  of  this  kind,  the  following  construction 
was  successfully  used : 

Instead  of  the  common  piles,  two  rows  of  iron  rods  were 
used.  These  rods  were  "jumped"  into  the  rock,  a  depth  of 
fifteen  inches.  The  sheet-piles  were  replaced  by  heavy  planks 
which  were  laid  in  a  horizontal  position  and  fastened  to  the 
rods  by  iron  rings.  This  method  of  fastening  allowed  the 
planks  to  be  pushed  down  until  each  one  rested  on  the  one 
below  it ;  the  plank  resting  on  the  bottom  being  cut  to  fit  the 
surface  of  the  rock. 

The  frame  was  strengthened  by  bolting  string  pieces  of 


300  CIVIL   ENGINEERING. 

timber  in  pairs  on  both  of  its  sides  and  by  using  inclined 
struts  upon  the  interior. 

The  puddling  was  of  the  usual  kind  and  was  put  in  the 
darn  in  the  way  already  described. 

417.  It  will  be  very  difficult  to  avoid  leakage  between  the 
bottom  of  the  puddling  and  the  soil  on  which  it  rests  unless 
the  stratum  of  overlying  soft  soil  be  removed.     It  is  therefore 
recommended  for  important  works  that  a  part  of  the  dredging 
for  this  purpose  be  done  before  the  common  piles  are  driven. 

Leakage  through  the  puddling  is  mostly  due  to  poor  work- 
manship. If  the  sheet-piles  are  fitted  and  carefully  driven, 
and  the  puddling  is  free  from  lumps  and  thoroughly  mixed, 
leakage  through  the  dam  should  not  occur.  It  is  not  advisa- 
ble to  have  bolts  or  rods  passing  through  the  dam,  as  leakage 
almost  invariably  takes  place  through  the  holes  thus  made. 
Fine  gravel  alone  has  been  proved  in  some  cases  to  be  a  better 
material  for  the  filling  than  ordinary  puddling. 

Leakage  due  to  springs  in  the  bottom  of  an  enclosed  area 
is  the  great  source  of  trouble,  and  in  some  soils  is  stopped 
with  much  difficulty.  It  may  be  necessary  to  fill  in  the  whole 
area  with  a  bed  of  concrete,  and  after  it  has  set  to  pump  out 
the  water. 

418.  The  water  having  been  pumped  out,  the  enclosed 
space  is  drained  into  some  convenient  spot  in  the  enclosure, 
and   arrangements  are  made  to  keep  the  interior  dry.     The 
bed  having  been  prepared,  the  masonry  is  then  built  to  the 
proper  height.     When  it  is  above  the  surface  of  the  water, 
the  dam  may  be  removed,  and  as  there  is  danger  of  disturbing 
the  bed  if  the  piles  were  drawn  out,  it  is  customary  to  cut 
them  off  at  some  point  below  the  water  line,  letting  the  lower 
ends  remain  as  driven. 

419.  Caisson  dams. — This  name  was  given  to  a  coffer-dam 
in  which  the  outer  row  of  common  piles  was  replaced  by 
structures  resembling  caissons,  which  were  sunk  and  ballasted 
to  keep  them  in  position  along  the  line  which  would  have 
been  occupied  by  the  common  piles. 

The  character  of  the  bottom  and  the  nature  of  the  stream 
were  such  that  common  piles  could  not  be  used  for  the  dam. 

The  caisson  (Fig.  149)  was  a  flat-bottomed  boat,  which  hav- 
ing been  floated  to  its  place  was  sunk  gradually,  by  the  ad- 
mission of  water,  until  it  rested  on  the  bottom.  A  row  of 
common  piles  was  then  placed  in  a  vertical  position  against 
each  side  of  the  caisson  and  lowered  until  they  rested  on  the 
bottom.  They  were  then  bolted  in  that  position  to  the  sides  of 
the  caisson.  The  caisson  was  then  heavily  loaded  with  stones 


CAISSON  DAMS. 


301 


and  other  weighty  materials,  until  a  considerable  weight  rested 
on  the  piles.  It  is  observed,  that  instead  of  the  piles  being 
held  fast  by  being  driven  into  the  ground,  they  are  held  in 
place  by  the  sunken  boat,  and  the  whole  arrangement  takea 
the  place  of  the  outer  row  of  piles  in  the  common  coffer-dam. 


FlG.  149 — Represents  a  cross-section  of  a  caisson  dam. 
A,  cross-section  of  caisson.  C,  puddling. 

D,  foundation  courses  of  the  pier. 

To  complete  the  dam,  a  row  of  posts,  parallel  to  the  inner 
row  of  piles,  resting  on  the  bottom  and  connected  by  a  frame- 
work with  the  caissons,  took  the  place  of  the  inner  row  of 
piles  in  the  common  coffer-dam. 

The  sheet-piles  were  required  only  on  the  one  side,  the 
sides  of  the  caissons  being  sufficient  on  the  other.  They  were 
laid  in  a  horizontal  position,  as  shown  in  the  figure.  The 
puddling  was  in  all  respects  the  same  as  that  described  in  the 
previous  cases. 

The  masonry  being  finished,  the  loads  were  removed  from 
the  caissons.  They  were  then  pumped  dry  and  the  dam  re- 
moved. 

420.  Crib-work  dam. — A  dam  in  which  a  crib  ballasted 
with  stone  takes  the  place  of  the  common  piles,  has  been  used 
with  success. 

In-  the  example  (Fig.  150).  the  cribs  were  built  by  laying 
the  logs  alternately  lengthwise  and  crosswise,  and  fastening 
them  together  at  their  intersections  by  notching  one  into  the 
other  and  pinning  them. 


302 


CIVIL    ENGINEERING. 


On  each  crib  a  platform  was  laid  about  midway  between 
the  top  and  bottom,  on  which  the  stone  was  placed  to  sink  the 
crib.  The  cribs  were  floated  to  the  place  they  were  to  occupy 
and  sunk  gradually  by  loading  stone  on  the  platform.  After 
they  had  been  fully  settled  in  their  place,  more  stones  were 
piled  on  until  the  required  stability  was  secured. 


FlG.  150 — Represents  a  cross-section  of  a  crib-work  dam. 

A,  inner  row  of  cribs.     B,  outer  row  of  cribs.     C,  puddling. 

Both  of  the  preceding  methods  were  used  in  constructing 
the  piers  and  abutments  of  the  Victoria  Bridge,  over  the 
Saint  Lawrence,  at  Montreal.  A  rocky  bottom,  covered  with 
boulders,  prevented  the  driving  and  the  use  of  the  common 
pile  as  in  the  ordinary  method.  There  was  also  in  the  river  a 
swift  current,  which  in  the  spring  of  the  year  brought  down 
large  quantities  of  ice,  the  effect  of  which  would  have  been 
to  have  destroyed  any  ordinary  caisson  or  common  coffer-dam. 

It  is  seen  that  these  dams  do  not  differ  in  principle  from 
the  common  coffer-dam,  and  that  the  modifications  in  each 
case  consisted  in  finding  for  the  common  pile  a  substitute 
which  would  be  stronger  and  equally  effective. 


H.    EXCLUSION   OF   WATER   FROM   THE    SITE   BY    ATMOSPHERIC 
PRESSURE. 

4:21.  In  recent  years,  the  use  of  compressed  air  has  been  ex- 
tensively adopted  as  a  means  for  excluding  the  water  from  the 
site  of  a  proposed  work,  while  the  bed  was  being  prepared. 

There  are  two  general  methods  of  its  application :  in  the 
pneumatic  pile  and  in  the  pneumatic  caisson. 

422.  Pneumatic  piles. — Pneumatic  piles  are  hollow  verti- 
cal cylinders  of  cast  iron,  from  six  to  ten  feet  in  diameter, 
intended  to  be  forced  through  soft  and  compressible  materials 
to  a  firm  soil  beneath,  and  to  be  then  entirely  filled  with 


PNEUMATIC   PILES. 


303 


masonry  or  concrete  or  other  solid  material.     Rankine  classes 
them  under  the  head  of  iron  tubular  foundations. 

Their  general  construction  and  the  mode  of  sinking  them 
in  the  soil  are  shown  in  Fig.  151. 


Fio.  151 — Represents  vertical  sec- 
tion of  a  pneumatic  pile. 

A,  body  of  cylinder. 

B,  the  bell. 

C,  elevation  of  air-lock. 

D,  vertical  section  of  air-lock. 

E,  water  discharge  pipe. 
M,  windlass  on  inside. 
N,  windlass  on  the  top. 

O,  O,  buckets  ascending  and  de- 
scending. 
W,W,  iron  weights. 


In  this  example,  shown  in  the  figure,  the  cylinders  were 
cast  in  lengths  of  nine  or  ten  feet,  with  flanges  on  the  interior 
at  each  end.  These  pieces  were  united  by  screw  bolts  passing 
through  holes  in  the  flanges,  the  joints  being  made  water, 
tight  either  by  an  india-rubber  packing  or  by  a  cement  made 
or  iron  turnings. 

To  sink  a  pile  of  this  kind,  a  strong  scaffolding  is  erected 
over  the  site,  and  from  which  the  lengths  of  the  cylinders  can 
be  lowered  and  placed  in  position.  On  this  scaffold  a  steam- 
engine  is  ordinarily  placed,  and  furnishes  the  power  required 
during  the  operation. 

The  lower  edge  of  the  lowest  section  of  the  cylinder  is 
sharpened  so  that  it  may  sink  more  easily  through  tfre  soiL 


304  CIVIL  ENGINEERING. 

The  upper  section,  termed  the  "bell,"  is  usually  made  of 
boiler  iron,  with  a  dome-shaped  or  flat  top.  An  "  air-lock  "  is 
used  to  pass  the  men  and  materials  in  and  out  of  the  cylinder. 
In  this  example  there  were  two  air-locks,  which  were  placed 
in  the  top  of  the  bell,  as  shown  in  the  figure.  Each  lock  had 
at  the  top  a  trap  door  which  opened  downwards,  and  at  the 
side  a  door  which  opened  into  the  interior  of  the  pile.  Stop- 
cocks were  provided  in  each,  communicating  with  the  ex- 
ternal air  and  the  interior  of  the  pile,  respectively ;  they 
could  be  opened  or  closed  by  persons  inside  the  tube,  within 
the  lock,  or  on  the  outside. 

The  bell  was  provided  with  a  supply  pipe  for  admission  of 
compressed  air,  a  pressure  gauge,  a  safety  valve,  a  large  escape 
valve  for  discharging  the  compressed  air  suddenly  when 
necessary,  and  a  water-discharge  pipe  about  two  or  three 
inches  in  diameter. 

Windlasses  placed  within  the  cylinder  and  on  the  outside, 
as  seen  in  the  figure,  were  used  to  hoist  the  buckets  employed 
in  the  excavation 

The  first  operation  in  sinking  the  pile  was  to  lower  the 
lowest  section,  with  as  many  additional  lengths  united  to  it  as 
were  necessary  to  keep  the  top  of  the  cylinder  two  or  three 
feet  above  the  surface  of  the  water,  until  it  rested  on  the 
bottom.  The  bell  and  one  additional  length  were  then  bolted 
to  the  top  of  the  pile. 

The  weight  of  the  mass  forced  it  into  the  soil  at  the  bot- 
tom of  the  river  a  certain  distance,  dependent  upon  the  na- 
ture of  the  soil.  As  soon  as  the  pile  stopped  sinking,  the  air 
was  forced  in  by  means  of  air-pumps  worked  by  the  steam- 
engine,  until  all  the  water  in  the  tube  was  expelled.  Work- 
men, with  the  proper  tools,  then  entered  the  cylinder  by 
means  of  the  air-locks. 

To  get  into  the  pile,  the  men  entered  the  lock,  closed  all 
communications  with  the  external  air,  and  then  opened  the 
stop-cock  communicating  with  the  interior  of  the  pile ;  in  a 
few  minutes  the  compressed  air  filled  the  lock,  the  men  opened 
the  side  door  and  thus  effected  an  entrance  into  the  interior. 
To  pass  out  it  was  only  necessary  to  reverse  this  operation. 

The  gearing  of  the  hoisting  apparatus  was  so  arranged  that 
the  buckets,  when  filled,  were  delivered  alternately  into  the 
locks,  and  were  then  hoisted  out  by  the  windlass  on  the  out- 
side. 

Care  was  taken  to  guard  against  the  uplifting  force  of  the 
compressed  air  within  the  pile.  In  the  above  example,  a 
heavy  weight,  composed  of  cast-iron  bars  resting  on  brackets 


PNEUMATIC   PILES.  305 

attached  to  the  outside  of  the  bell,  was  used  to  resist  this 
action. 

The  workmen  having  descended  to  the  bottom  of  the  pile, 
excavated  the  material  to  the  lower  edge ;  they  then  took  off 
the  lowest  joint  of  the  water  discharge  pipe  and  carried  it 
and  their  tools  to  the  bell,  and  passed  out  of  the  lock.  The 
valve  for  admitting  compressed  air  was  then  closed  and  the 
large  escape  valve  opened,  allowing  the  compressed  air  to 
escape.  The  cylinder  being  deprived  of  the  support  arising 
from  the  compressed  air,  sank  several  feet  into  the  soil,  the 
distance  depending  on  the  resistance  offered  by  the  soil. 

When  the  pile  had  stopped  sinking,  the  escape  valve  was 
closed,  the  air  forced  in,  and  the  operations  just  described 
continued.  Great  care  was  taken  to  keep  the  pile  in  a  verti- 
cal position  while  sinking. 

The  pile,  having  reached  the  required  depth,  was  then  filled 
with  concrete. 

The  usual  method  of  filling  the  pile  is  to  perform  about 
one-half  of  the  work  in  the  compressed  air  and  then  remove 
the  bell  and  complete  the  rest  in  the  open  air.  In  filling  with 
concrete,  it  should  be  well  rammed  under  the  flanges  and 
around  the  joints. 

423.  This  description  of  a  pneumatic  pile,  just  given,  is 
that  of  one  of  the  piles  used  in  the  construction  of  a  bridge 
over  the  river  Theiss,  at  Szegedin,  in  Hungary. 

The  river,  at  this  point,  has  a  sluggish  current  with  a  gra- 
dual rise  and  fall  of  the  water,  the  difference  between  the 
highest  and  lowest  stages  of  water  being  about  twenty-six  feet. 
The  soil  of  the  bottom  is  alluvial,  composed  to  a  great  depth 
of  alternate  strata  of  compact  clay  and  sand. 

The  piles  were  sunk  to  about  thirty  feet  below  the  bottom  of 
the  river,  which  latter  was  about  ten  feet  deep  at  low  water. 

The  excavation  was  carried  down  to  within  six  feet  of  the 
bottom  of  the  pile.  Twelve  common  piles  of  pine  were  then 
driven  within  the  cylinder,  extending  to  a  depth  of  twenty 
feet  below  it.  The  concrete  was  then  thrown  in  and  rammed 
in  layers  until  its  upper  surface  was  on  a  level  with  that  of 
ordinary  low  water. 

The  air-locks  were  about  six  feet  and  a  half  high  and  two 
and  three-quarters  in  diameter. 

424.  In  the  first  uses  of  the  pneumatic  piles,  the  cylinders 
were  of  small  size,  as  many  being  sunk  as  were  required  to 
support  the  load,  as  in  the  use  of  common  piles. 

They  wero  sunk  into  the  soil  by  exhausting  the  air  from 
the  interior.     The  result  following  this  removal  of  air  was  tint 
20 


306  CIVIL  ENGINEERING. 

the  earth  immediately  under  the  pile  was  forced  togethei  with 
water,  into  the  inside  of  the  cylinder,  and  the  pile  sank  into 
the  opening  thus  made,  both  under  its  own  weight  and  the 
pressure  of  the  atmosphere. 

This  process  is  known  as  Dr.  Pott's,  and  is  well  adapted  to 
soft  or  sandy  soils,  when  free  from  stones,  roots,  pieces  of  tim- 
ber, etc.  The  presence  in  the  soil  of  any  obstacle  which  the 
edge  of  the  tube  cannot  cut  through  or  force  aside,  renders 
this  method  impracticable. 

The  next  step  was  to  increase  the  size  of  the  pile,  and  in- 
stead of  exhausting  the  air,  to  fill  it  with  compressed  air. 
The  top  being  closed  and  the  bottom  open,  all  fluid  matter 
was  driven  from  the  interior  of  the  pile  by  the  compressed 
air.  By  means  of  air-locks  on  the  top  of  the  cylinder,  work- 
men were  enabled  to  descend  and  remove  the  soil  and  such 
obstructions  as  prevented  the  pile  from  sinking.  This  pro- 
cess is  generally  known  as  "  Triger's." 

The  air  being  compressed  in  the  interior  of  the  pile,  the 
weight  or  the  pressure  downward  was  much  lessened.  To 
increase  the  pressure  a  weight  was  placed  on  the  pile. 

Although  many  improvements  have  been  made  in  the  de- 
tails, the  arrangements  just  described  illustrate  the  general 
outline  of  all  the  pneumatic  methods  in  use. 

425.  Pneumatic  method  used  by  Mr.  Brunei. — The  first 
improvement  in  the  pneumatic  method  was  that  used  by  Mr. 
Brunei  in  preparing  the  bed  for  the  centre  pier  of  the  Koyal 
Albert  Bridge,  at  Saltash,  England. 

This  improvement  consisted  in  confining  the  compressed 
air  to  a  chamber  at  the  bottom  of  a  cylinder,  the  rest  of  the 
space  inside  of  the  cylinder  being  open  to  the  air.  The  air 
chamber  communicated  with  the  outside  air  by  means  of  a 
tube,  six  feet  in  diameter,  with  air-locks  at  the  upper  end. 
Outside  of  this  tube,  was  another  tube,  ten  feet  in  diameter, 
connecting  the  dome  with  the  outside  air.  (Fig.  152.) 

A  dome,  about  25  feet  high,  was  built  in  the  lower  portion, 
BO  arranged  that  the  top  of  the  dome  should  be  above  the 
mud  when  the  cylinder  rested  on  the  rock. 

The  chamber  for  the  compressed  air  was  annular,  four 
feet  wide,  twenty  feet  high,  was  built  around  the  inner  cir- 
cumference of  the  lower  edge  and  was  divided  into  eleven 
compartments  by  vertical  and  radial  partitions;  apertures 
in  the  partitions  afforded  communications  from  one  to  the 
other.  An  air  passage  at  the  top  of  the  compartments  con- 
nected them  with  each  other,  and  with  the  vertical  tube  of 
six  feet  diameter  before  alluded  to. 


PNEUMATIC   PILES. 


307 


The  cylinder  was  lowered  into  the  water  exactly  over  the 
place  it  was  to  occupy.  As  soon  as  it  stopped  sinking,  the 
annular  chamber  was  shut  off  from  the  rest  of  the  dome,  the 
air  forced  in,  the  water  driven  out,  the  workmen  descended 
and  dug  out  the  mud  and  loose  soil  under  the  edge. 


FIG.  152 — Represents  a  longitudinal  section 
through  the  axis  of  the  cylinder.  The 
cylinder  was  37  feet  in  diameter,  about 
100  feet  high,  made  of  boiler  iron,  and 
weighed  nearly  300  tons.  The  rock  on 
which  it  was  to  rest  was  about  90  feet 
below  the  surface  of  the  water,  overlaid 
with  about  20  feet  of  loose  sand  and  mud. 
The  rock  surface  had  a  slight  slope,  to 
which  the  bottom  of  the  cylinder  was 
made  to  fit. 


When  the  rock  was  reached,  a  level  bed  was  cut  in  its  sur- 
face and  a  ring  of  masonry  built.  The  water  was  then  pumped 
out  of  the  main  tube  and  the  masonry  begun  on  the  inside. 
As  the  masonry  rose,  the  partitions,  shaft,  and  the  dome  were 
removed.  When  the  pier  was  above  the  surface  of  the  water, 
the  upper  part  of  the  cylinder,  about  fifty  feet  in  length,  was 
unbolted  and  taken  away,  it  having  been  made  in  two  sections 
for  this  purpose. 

As  the  volume  of  the  annular  chamber  in  which  the  com- 
pressed air  was  used  was  small  in  comparison  with  the  vol- 
ume of  the  main  cylinder,  no  extra  weight  was  needed  to 
balance  the  upward  pressure. 

The  above  is  a  good  example  of  the  pneumatic  process 
combined  with  the  principle  of  the  coffer-dam. 


308  CIVIL   ENGINEERING. 

426.  Pneumatic  caisson. — The  next  important  modifica- 
tion in  the  pneumatic  method  was  to  combine  the  principle 
of  the  diving-bell  with  that  of  the  common  caisson.    This  com- 
bination is  known  as  the  pneumatic  caisson  and  furnishes 
the  means  now  most  commonly  used  in  situations  like  that  at 
the  Saltash  bridge,  and  especially  where  the  foundations  have 
to  support  a  great  pressure. 

It  consists  essentially  of  three  parts:  1st,  The  caisson; 
2d,  The  working  chamber ;  and  3d,  The  pneumatic  ap- 
paratus and  its  communications  with  the  working  chamber. 

Caisson. — This  does  not  differ  in  its  principles  of  construc- 
tion from  the  common  caisson  already  described.  The  bottom 
is  of  wood  or  iron,  made  strong  enough  to  support  the  struc- 
ture with  its  load,  and  forms  the  roof  of  the  working  chamber. 
The  sides  are  generally  of  wrought  iron,  and  are  not  usually 
detached  from  the  bottom  when  the  structure  is  finished. 

Working  chamber. — This  is  below  the  caisson,  and  as  just 
stated,  the  bottom  of  the  caisson  is  the  roof  of  the  chamber. 
Its  sides  are  firmly  braced  to  enable  it  to  resist  the  pressure 
from  both  the  earth  and  water  as  it  sinks  into  the  ground. 
The  chamber  is  made  air  and  water  tight. 

Pneumatic  apparatus  and  communications. — Vertical 
shafts,  either  of  iron  or  masonry,  passing  through  the  roof  of 
the  chamber  furnish  the  means  of  communication  between 
the  working  chamber  and  the  top  of  the  caisson.  The  air- 
locks may  be  placed  in  the  upper  end  of  the  shaft,  as  in  the 
pneumatic  pile,  or  at  the  lower  end  of  the  shaft  where  it  con- 
nects with  the  working  chamber. 

The  usual  supply  pipes,  air-pumps,  discharge  pipes,  etc.,  are 
required  as  in  the  other  pneumatic  methods. 

Sinking  the  caisson. — It  is  moored  over  the  place  it  is  tc 
occupy  and  is  sunk  gradually  to  the  bottom  as  an  ordinary  cais- 
son. Air  is  then  forced  into  the  working  chamber,  driving 
out  the  fluid  matter;  the  earth  and  loose  material  are  then  dug 
out,  while  the  caisson  settles  slowly  under  its  own  weight  and 
that  of  the  masonry  until  it  rests  on  the  firm  soil  or  solid  rock. 

An  outline  description  of  some  of  the  caissons  recently 
used  will  more  fully  illustrate  their  construction  and  the 
method  of  sinking  them. 

427.  Pneumatic  caissons  used  at  L'Orient,  France. — 
These  were  used  in  laying  the  foundations  of  two  of  the  piers 
of  a  railroad  bridge  over  the  river  Scorff,  at   L'Orient,  in 
France.     The  river  bed  consisted  of  mud  from  25  to  45 
feet  deep,  lying  upon  a  hard  rock.     The  surface  of  the  water 
was  about  60  feet  above  the  rock  at  mean  tide,  and  70  feet  al 


PNEUMATIC   CAISSONS. 


309 


high  tide.  It  was  essential  for  the  stability  of  the  piers  that 
they  should  rest  on  the  rock. 

The  caissons  used  were  40  feet  long,  12  feet  wide,  and 
made  of  boiler  iron. 

The  thickness  of  the  iron  forming  the  sides  of  the  caisson 
varied  according  to  the  depth  in  the  water,  being  greater  for 
the  lower  than  for  the  middle  and  upper  parts.  The  ratio  of 
the  thickness  was  for  the  upper,  middle,  and  lower,  as  3,  4, 
and  5. 

The  working  chamber  was  ten  feet  high  and  communicated 
with  the  upper  chamber  or  bells,  where  the  air-locks  were 

E  laced,  by  two  tubes  for  each  bell ;  these  tubes  were  each  two 
3et  and  three-quarters  in  diameter.     Each  bell  was  ten  feet 
high  and  eight  feet  in  diameter,  and  contained  two  air-locks 
and  the  necessary  hoisting  gear ;  the  full  buckets  ascended 
through  one  tube  and  descended  through  the  other. 

Fig.  153  shows  the  caisson  used  for  the  pier  on  the  right 
bank. 


FIG.  153 — Represents  a  vertical  section 
of  caisson  and  masonry  of  pier  during 
the  process  of  sinking. 

A,  the  working  chamber. 

B,  interior  elevation  of  caisson. 
C,C,  elevation  of  the  bells. 
D,D,  the  communicating  tubes. 

E,E,  masonry  of  pier,  built  as  the  caison 
was  sinking. 


When  the  rock  was  reached,  its  surface  was  cleaned  off 
and  a  level  bed  made  under  the  edges  of  the  caisson.  The 
working  chamber  was  then  filled  up  to  the  roof  with  ma- 
sonry. * 

The  pier  was  of  concrete  with  a  facing  of  stone  masonry, 
and  built  up  as  the  caisson  was  sinking  to  its  place. 

The  working  chamber  being  filled,  the  tubes  were  with- 
drawn and  the  spaces  occupied  by  them  filled  with  con 
crete. 


310 


CIVIL   ENGINEERING. 


Pneumatic  Caissons  at  St.  Louis,  Mo. 

428  At  the  time  the  foundations  of  the  piers  of  the  bridge 
over  the  Mississippi  River,  at  St.  Louis,  were  laid,  the  caissons 
there  used  were  the  largest  that  had  ever  been  employed  for 
such  a  purpose. 

This  bridge  consists  of  three  spans,  supported  on  two  piers 


PlG.  154 — Represents  a  section  of  the  caisson  used  in  construc- 
tion of  east  pier  of  the  bridge  over  the  Mississippi 
River,  at  St.  Louis,  Mo. 

A,  main  shaft.     B,  air-locks.     C,  working  chamber. 

D,  sides  of  caisson.     E,  side  shafts.     F,  sand  pumps. 

G,  discharge  of  sand. 

and  the  abutments.  The  river  at  this  point  is  2,200  feet  wide 
at  high  water,  with  a  bed  of  sand  over  rock.  The  rock  slopes 
from  the  west  to  the  east,  the  upper  surface  of  the  sand  being 
practically  level.  The  depth  of  the  sand  on  the  western  shore 
was  about  15  feet,  and  on  the  eastern  nearly  100  feet. 


PNEUMATIC  CAISSONS.  311 

As  the  scour  on  the  bottom  is  very  great  in  the  Mississippi 
River,  it  was  regarded  as  essential  that  the  piers  should  rest  on 
the  rock.  To  penetrate  this  sand  and  lay  the  foundations  on 
the  rock,  the  pneumatic  caisson  was  used. 

Fig.  154  represents  a  section  of  the  one  used  for  the  east 
pier.  There  the  rock  was  128  feet  below  the  high- water 
mark.  When  the  caisson  was  moored  in  position  there  was 
above  the  rock  35  feet  of  water  and  68  feet  of  sand. 

The  plan  of  the  caisson  was  hexagonal,  the  long  sides  beincj 
50  feet  each,  and  the  short  ones  35  feet  each.  The  sides  of 
the  caisson  were  made  of  plate  iron,  three-eighths  of  an  inch 
in  thickness,  and  built  up  as  the  caisson  sank. 

The  bottom,  which  was  to  support  the  masonry,  was  com- 
posed of  iron  girders,  placed  5£  feet  apart.  Iron  plates, 
\  inch  thick,  were  riveted  to  the  under  side  of  these  girders 
to  form  the  roof  of  the  working  chamber.  The  sides  of  the 
caisson,  prolonged  below  the  girders,  formed  the  sides  of  the 
chamber,  and  were  strongly  braced  with  iron  plates  and  stif- 
fened by  angle  irons.  The  chamber,  thus  formed,  was  80 
feet  long,  60  feet  wide,  and  had  an  interior  height  of  9  feet. 
The  interior  space  was  divided  into  three,  nearly  equal,  parts 
by  two  heavy  girders  of  timber  placed  at  right  angles  to 
those  of  iron,  and  intended  to  rest  on  the  sand  and  assist 
in  supporting  the  roof  of  the  chamber.  Openings  made 
through  the  girders  allowed  free  communication  between  the 
divisions. 

Access  to  the  top  of  the  caisson  was  obtained  by  vertical 
shafts  lined  with  brick  masonry,  and  passing  through  the  roof 
of  the  chamber.  The  air-locks  were  at  the  lower  end  of  the 
shafts  and  within  the  chamber. 

As  the  caisson  descended,  the  masonry  pier  was  built 
up  in  the  usual  manner,  its  foundation  resting  on  the  iron 
girders. 

In  the  chamber  were  workmen  who  excavated  the  sand, 
and  shovelled  it  under  the  sand-pumps.  (Fig.  154.)  A 
pump  of  3£  inches  diameter,  working  under  a  pressure  of  150 
pounds  on  the  square  inch,  was  capable  of  raising  20  cubic 
yards  of  sand  125  feet  per  hour. 

When  the  caisson  reached  the  rock,  the  latter  was  cleared 
of  sand  and  the  entire  chamber  then  filled  with  concrete. 

The  experience  acquired  in  sinking  this  caisson  enabled  the 
engineer  to  make  material  modifications  in  the  details  of  the 
caissons  subsequently  used. 

The  health  of  the  workmen  was  greatly  affected  by  the 
high  degree  of  compression  of  the  air  in.  which  they  had  to 


312  CIVIL   ENGINEERING. 

work.  In  some  cases  the  pressure  was  as  high  as  fifty  pounds 
on  the  square  inch,  and  several  lost  their  lives  in  consequence. 
In  the  second  pier,  instead  of  filling  the  chamber  entirely 
with  concrete  when  the  rock  was  reached,  the  space  around 
the  edges  was  only  closed  with  concrete  and  the  cnamber  was 
then  filled  with  clean  sand. 


Pneumatic  Caisson  at  St.  Joseph,  Mo. 

429.  This  was  used  in  1.871-2  in  laying  the  foundations  of 
the  piers  for  a  railroad  bridge  over  the  Missouri  River,  at  St. 
Joseph,  Mo. 

For  a  reason  similar  to  that  given  in  the  last  case,  it  was 
decided  to  rest  the  piers  on  the  rock  below  the  bottom  of  the 
river.  The  rock  was  about  sixty-seven  feet  below  the  level 
of  high  water,  and  was  overlaid  with  mud  and  sand  to  depths 
varying  from  forty  to  the  whole  distance  of  sixty -seven  feet. 
Six  piers  were  used  and  were  placed  in  depths  of  water  vary- 
ing at  the  low  stage  from  zero  to  twenty-five  feet ;  the  differ- 
ence between  high  and  low  water  being  twenty-two  feet. 
Pockets  of  clay,  with  occasionally  snags  and  boulders,  were 
met  with  in  the  sand  and  mud. 

The  caisson  used  for  pier  No.  4  was  made  of  twelve-inch 
square  timber,  and  was  at  the  bottom  fifty-six  feet  long,  and 
twenty-four  feet  wide.  The  sides  of  the  working  chamber 
were  three  feet  thick,  sloping  inwards  with  a  batter  of 
ig-.  It  was  built  by  placing  a  row  of  timbers  in  a  vertical 
position,  side  by  side,  for  the  outside ;  then,  inside  of  this, 
a  second  row  was  laid  horizontally ;  and  then,  for  the  inside, 
a  third  row  in  a  vertical  position.  The  outer  row  extended 
one  foot  below  the  middle  row,  and  the  latter  one  foot 
below  the  third.  A  horizontal  beam  extending  entirely 
around  the  interior  was  bolted  to  the  sides  of  the  chamber, 
one  foot  above  the  bottom  of  the  inside  row.  A  set  of  in- 
clined struts  rested  on  this  beam,  and  abutted  against  strain- 
ing beams  framed  into  the  roof  of  the  chamber.  The  roof 
was  solid  timber,  four  feet  thick,  on  which  rested  the  grillage 
for  the  masonry  of  the  pier.  The  grillage  was  made  of  tim- 
ber, seven  courses  thick,  each  course  being  laid  at  right 
angles  to  the  one  below  it.  The  timbers  of  each  course  were 
separated  by  a  space  of  six  inches,  excepting  the  top  course, 
which  was  solid. 

All  the  timber  work  was  accurately  fitted,  and  the  whole 


PNEUMATIC   CAISSONS.  313 

bolted  together  so  as  to  form  one  unyielding  mass.  The 
interior  of  the  working  chamber  was  calked,  and  was  prac- 
tically air-tight.  The  dimensions  of  the  chamber  were,  on 
the  inside,  twenty-two  feet  wide  and  fifty-four  long  at  the 
bottom :  five  feet  wide  and  seven  feet  long  at  the  top  ;  and 
nine  feet  high  at  the  centre.  The  grillage  was  drawn  in  so 
that  its  top  was  of  the  same  dimensions  as  the  base  of  the 

gier,  being  nine  feet  wide  and  twenty  long,  with  curved  star- 
ngs  at  each  end. 

The  air-lock  was  four  feet  in  diameter  and  seven  high, 
made  of  plate  iron,  and  placed  in  the  middle  of  the  top  of 
the  chamber.  A  door  in  the  top  of  the  air-lock  opening 
downwards  communicated  with  a  vertical  iron  shaft  three  feet 
in  diameter;  the  shaft  extended  above  the  top  of  the  ma- 
sonry and  allowed  access  to  the  top  of  the  caisson.  An  iron 
ladder  in  the  shaft  was  used  for  ascent  and  descent.  The 
usual  supply  and  discharge  pipes  passed  through  the  grillage 
to  the  working  chamber. 

The  caisson  was  sunk  by  the  process  previously  described. 
The  arrangement  of  the  lower  bearing  surfaces  of  the  cais- 
son are  regarded  as  worthy  of  notice.  The  lower  edge  of 
the  outside  row  of  timbers  was  sharpened ;  as  soon  as  it  had  . 
sunk  one  foot,  the  under  surface  of  the  second  or  horizontal 
row  came  into  play,  adding  a  foot  of  bearing  surface.  When 
the  caisson  had  descended  two  feet,  the  bottom  of  the  inside 
or  third  row  pressed  on  the  soil,  thus  giving  three  feet  of 
bearing  surface.  By  this  arrangement  the  amount  of  bearing 
surface  was  under  the  control  of  the  engineer.  If  the  soil 
through  which  the  caisson  was  sinking  was  variable  in  its  na- 
ture, that  is,  if  on  one  side  of  the  caisson  it  was  soft,  and  on 
the  other  it  was  hard,  the  bearing  surface  could  be  increased 
on  the  soft  side  and  diminished  on  the  other.  In  this  way 
the  caisson  could  be  kept  vertical  while  sinking. 

The  greater  part  of  the  material  excavated  was  mud  or 
sand,  and  was  discharged  easily  arid  rapidly  by  means  of 
sand  pumps.  The  clay,  boulders,  and  snags  were  discharged 
through  the  air-lock. 

The  caisson  was  sunk  at  the  rate  of  from  five  to  seven  feet 
in  twenty-four  hours. 

When  the  caisson  reached  the  bed  rock,  a  wall  of  concrete, 
six  feet  thick,  was  built  on  the  rock  under  the  edges,  and 
was  solidly  rammed  under  the  three  rows  of  timbers  and  up 
to  and  including  the  horizontal  beam  supporting  the  struts. 
Strong  vertical  posts  were  placed  under  the  roof  to  assist  in 
supporting  it.  The  sand  pumps  were  then  reversed,  and  the 


314  CIVIL  ENGINEERING. 

chamber  was  filled  with  clean  sand  and  gravel.  A  tube  was 
so  placed  as  to  allow  the  escape  of  the  water  in  the  sand,  so 
that  the  whole  interior  was  compactly  filled  with  solid  mate- 
rial. The  sand  pumps  were  then  withdrawn,  and  the  shafts 
themselves  were  filled. 

Caissons  of  the  East  River  Bridge  at  New  York. 

430.  The  caissons  used  for  the  foundations  of  the  piers  in 
this  bridge  were  rectangular  in  form,  and  made  of  timber. 

The  exterior  of  the  bottom  of  the  chamber  in  the  Brooklyn 
caisson  was  168  feet  long  and  102  wide.  In  the  one  on  the 
New  York  side  the  width  was  the  same,  but  the  length  was 
four  feet  greater. 

Both  were  nine  and  a  half  feet  high  on  the  inside.  The 
roof  of  the  Brooklyn  caisson  was  a  solid  mass  of  timber,  fif- 
teen feet  thick  (Fig.  155),  and  of  the  New  York  caisson, 
twenty-two  feet  thick. 


FlG.  155 — Represents  section  through  water  shaft  of  the  Brooklyn  caisson, 
showing-  method  of  removing  boulders  or  other  heavy  materials. 

The  sides  of  the  caisson  had  a  slope  of  -L-0-  for  the  outer 
face,  and  of  -J-  for  the  inner,  as  shown  in  the  figure.  The  outer 
slope  was  for  the  purpose  of  facilitating  the  descent  of  the 
caisson  into  the  ground.  The  lower  edge  was  of  cast  iron, 
protected  by  boiler  iron,  extending  up  the  sides  for  three  feet. 
The  sides,  where  they  joined  the  roof,  were  nine  feet  thick. 
The  chambers  were  calked  both  on  the  outside  and  inside,  to 
make  them  air-tight.  As  a  farther  security,  an  unbroken 
sheet  of  tin  extended  over  the  whole  roof  between  the  fourth 
and  fifth  courses,  and  down  the  sides  to  the  iron  edge.  The 
New  York  chamber  was,  in  addition,  lined  throughout  on  the 
inside  with  a  light  iron  plate,  to  protect  it  from  fire. 


MOVABLE  PNEUMATIC   CAISSON.  315 

Each  chamber  was  divided  by  five  solid  timber  partitions 
into  six  compartments,  each  from  twenty-five  to  thirty  feet 
wide.  Communication  from  one  to  the  other  was  effected  by 
doors  cut  through  the  partitions. 

The  air-locks  were  placed  in  the  roof,  projecting  into  the 
chamber  four  feet,  and  communicating  at  the  top  with 
vertical  shafts  of  iron,  built  up  as  the  caisson  descended. 
The  locks  were  eight  feet  high  and  six  and  a  half  feet  in  dia- 
meter. 

The  mud  and  sand  were  discharged  through  pipes  by  the 
compressed  air.  A  pipe,  three  and  a  half  inches  in  diameter, 
discharged  sand  from  a  depth  of  sixty  feet  at  the  rate  of  one 
cubic  yard  in  two  minutes,  by  the  aid  of  the  compressed  air 
alone. 

The  heavy  materials  were  removed  through  water  shafts. 
These  were  seven  and  three-quarter  feet  in  diameter,  open  at 
the  top  and  at  the  lower  end,  the  latter  extending  eighteen 
inches  below  the  general  level  of  the  excavation.  A  column 
of  water,  in  the  shaft,  prevented  the  compressed  air  from 
escaping. 

Tne  material  to  be  removed  through  the  water  shaft  was 
thrown  into  an  excavation  under  the  lower  end  of  the  shaft ; 
it  was  there  grasped  by  a  "  grapnel  bucket,"  which  was  low- 
ered through  the  shaft,  and  hoisted  through  the  water  to  the 
top  of  the  shaft,  where  it  was  removed. 

After  the  caisson  had  reached  the  rock,  the  chamber  was 
filled  with  concrete,  in  the  usual  manner. 

The  great  thickness  of  the  roof,  and  the  moderate  depth  of 
water,  enabled  the  engineer  to  dispense  with  the  use  of  sides 
to  the  caisson,  as  the  masonry  could  be  kept  always  above  the 
surface  of  the  water. 

Movable  Pneumatic  Caisson. 

431.  A  pneumatic  caisson  has  been  successfully  used  in 
laying  the  foundations  of  piers  of  bridges,  which  differs  from 
those  already  described,  in  its  construction  admitting  of  its 
being  moved  after  completion  of  one  pier,  to  another  place  for 
the  same  purpose.  It  was  an  iron  cylinder,  ten  feet  in  dia- 
meter (Fig.  156),  connected  at  its  lower  end  with  a  working 
chamber,  eight  feet  high  and  eighteen  feet  in  diameter.  On 
the  roof  of  the  latter  was  another  chamber,  annular  in  form, 
eighteen  feet  in  diameter  and  about  six  feet  high,  so  arranged 
as  to  allow  of  being  filled  with  water  when  any  additional 
weight  was  necessary,  and  being  emptied  of  water  and  its 


316 


CIVIL   ENGINEERING. 


place  supplied  with  compressed  air  when  less  weight  was  de- 
sired. On  top  of  this  annular  chamber  was  a  similar  one  ar- 
ranged to  be  loaded  with  iron  ballast.  Strong  chains  attached 
to  the  roof  of  the  working  chamber  and  connected  with  a 
hoisting  apparatus,  placed  on  a  strong  scaffolding  over  the 
site  of  the  pier,  were  used  to  lower  and  lift  the  cylinder,  as 
necessity  required. 


FIG.  156— Represents  section   of  moT- 

able  pneumatic  caisson. 
B,  working  chamber. 
A,  chamber  for  water,  or  for  compressed 

air. 

W,  chamber  for  iron  ballast, 
c,  c,  elevation  of  lengths  of  the  iron 

cylinder. 


Air-locks,  air-pumps,  and  all  the  necessary  adjuncts  of  a 
pneumatic  pile,  were  provided  and  used.  Having  reached  the 
rock  or  firm  soil,  the  bed  and  the  foundations  were  con- 
structed as  already  described.  As  the  masonry  of  the  pier 
rose,  the  whole  apparatus  was  lifted  by  the  chains  and  hoist- 
ing apparatus,  the  cylinder  being  lightened  by  expelling  the 
water  from  the  chamber,  A,  and  filling  the  latter  with  com- 
pressed air.  The  masonry  of  the  pier  having  risen  above  the 
surface  of  the  water,  the  whole  apparatus  was  removed  and 
used  in  another  place. 

432.  Remark. — It  is  seen  that  the  pneumatic  caisson,  as 
before  stated,  is  simply  a  combination  of  the  diving-bell  with 
the  common  caisson,  the  diving-bell  being  on  a  large  scale, 
and  its  roof  being  intended  to  form  a  part  of  the  bed  of  the 
foundation. 

Experience  has  shown  that  the  large  caissons  are  more 
easily  managed  than  the  small  ones.  The  circumstances  of 
the  case  can  only  decide  as  to  which  is  preferable,  the  caisson 
or  the  pneumatic  pile.  Either  method  is  an  expensive  one, 


PROTECTING   THE   FOUNDATION   BED.  317 

and  is  only  employed  in  localities  where  the  others  are  not 
applicable. 

SECURING  THE  BED  FROM  THE   INJURIOUS  ACTION  OF 

WATER. 

433.  The  bed  of  a  river  composed  of  sand  or  gravel  is  liable 
to  change  from  time  to  time,  as  these  materials  are  moved 
by  currents  in  the  river.  This  change,  when  accompanied  by 
an  increase  in  depth  of  the  river,  is  known  as  the  "  scour." 
Sometimes  a  scour  will  occur  on  one  side  of  a  structure  and 
not  on  the  other,  producing  an  undermining  threatening  the 
stability  of  the  masonry.  Where  common  piles  have  been  used, 
they  have  occasionally  been  washed  out  by  this  action.  Even 
in  rocky  bottoms,  when  of  loose  texture,  the  rock  will  gradu- 
ally wear  away  under  the  action  of  currents,  unless  protected 

It  therefore  becomes  an  important  point  to  provide  security 
for  the  beds  in  all  soils  liable  to  any  change.  It  is  for  this 
reason  that  in  very  important  structures,  the  foundations  are 
placed  on  the  bed  rock  far  below  the  possible  action  of  cur- 
rents, and  so  arranged  that  even  if  they  should  be  exposed  to 
a  scour  they  would  be  safe.  This  requirement  has  caused  the 
free  use  of  the  pneumatic  methods. 

Various  expedients  have  been  used  to  secure  the  beds  where 
they  do  not  rest  on  the  rock  or  on  a  soil  below  the  action  of 
the  water.  A  common  method  is  to  rip-rap  the  bed,  that  is, 
to  cover  the  surface  of  the  bottom,  around  the  bed,  with  frag- 
ments of  stone  too  large  to  be  moved  by  the  currents,  and  if 
the  soil  is  a  sand  or  loose  gravel,  to  use  clay  in  connection 
with  the  stone  to  bond  the  latter  together. 

Where  the  bed  is  made  of  piles,  it  is  well  to  enclose  the 
piles  by  a  grating  of  heavy  timber,  before  throwing  in  the 
stone.  In  some  cases  the  foundations  are  boxed,  that  is,  the 
piles  are  enclosed  by  a  sheeting  of  planks,  or  by  other  device, 
BO  as  to  protect  them  from  the  scour. 


PART   VI. 

BRIDGES. 

CHAPTER  XIII. 

434.  A  "bridge  is  a  structure  so 'erected  over  a  water-course, 
or  above  the  general  surface  of  the  ground,  as  to  afford  a  con- 
tinuous roadway  between  the  opposite  sides  of  the  stream,  or 
above  the  surface  of  the  country,  without  obstructing  those 
lines  of  communication  lying  beneath. 

Such  a  structure,  thrown  over  a  depression  in  which  there 
is  ordinarily  no  water,  is  generally  called  a  viaduct. 

If  the  structure  supports  an  artificial  channel  for  conveying 
water,  it  is  known  as  an  aqueduct;  and  where  it  crosses  a 
stream,  it  is  frequently  called  an  aqueduct-bridge. 

Bridges  may,  for  convenience  of  description,  be  classed 
either  from  the  materials  of  which  they  are  made:  as 
masonry  or  stone,  iron,  wooden  bridges,  etc. ;  or  from  the 
character  of  the  structure  :  as  permanent,  movable,  float- 
ing bridges,  etc. ;  or  from  the  general  mechanical  principles 
employed  in  arranging  its  parts :  as  arched,  trussed,  tubular 
bridges,  etc. 

435.  Component  parts. — A  bridge  consists  of  three  es- 
sential parts : 

1st,  The  piers  and  abutments  on  which  the  superstruc- 
ture rests ;  2d,  the  frames  or  other  arrangements  which  sup- 
port the  roadway ;  and  3d,  the  roadway,  with  the  parts  used 
in  connection  with  it  for  its  preservation  or  to  increase  its 
security,  as  the  roof,  parapets,  etc. 

Bridges  are  of  various  kinds,  both  in  their  general  plan  and 
dimensions.  The  latter  are  dependent  upon  the  objects  of 
and  the  circumstances  requiring  the  erection  of  the  bridge. 

The  simplest  bridge  is  one  in  which  the  points  of  support 


PIERS   AND   ABUTMENTS.  319 

are  so  near  together  that  two  or  more  simple  beams  laid 
across  the  stream,  or  across  an  opening  to  be  passed  over,  are 
sufficient  for  the  frame ;  a  few  planks  laid  upon  the  beams 
may  then  form  the  roadway. 

The  supports  being  strong  enough,  the  proper  dimensions 
for  the  beams  and  for  the  planking  are  easily  determined. 

This  calculation  for  the  beams  is  made  under  the  hypo- 
thesis that  each  is  a  simple  beam,  resting  on  two  points  of 
support  at  the  extremities,  strained  by  a  load  uniformly  distrib- 
uted over  it,  and  also  by  a  weight  acting  at  the  middle  point. 

The  uniform  load  is  the  weight  of  the  structure,  ordinarily 
assumed  to  be  uniformly  distributed  in  the  direction  of  its 
length.  The  weight  at  the  middle  represents  the  heavy  body 
as  it  passes  over  ;  as,  for  example,  a  heavily  loaded  wagon  for 
a  common,  and  a  locomotive  for  a  railroad  bridge.  Having 
determined  what  this  weight  shall  be,  its  equivalent  uniform 
load  may  be  obtained,  and  added  to  that  already  assumed ;  or 
if  preferred,  the  uniform  load  may  be  replaced  by  its  equiva- 
lent weight  at  the  middle. 

If  the  number  of  these  beams  be  represented  by  yi,  and  we 
suppose  that  they  are  at  equal  distances  apart,  then  the  total 
load  on  the  bridge  divided  by  n  will  give  the  load  on  each 
beam.  Then  by  formulas  already  deduced  we  can,  knowing 
the  value  for  R,  determine  the  proper  breadth  and  thickness 
for  each  beam. 

436.  Platform  of  roadway. — In  a  common  wooden  bridge 
the  roadway  is  generally  of  planks.     These  are  of  hard  wood, 
from   three   to  four  inches   thick,   resting  on   longitudinal 
pieces  placed  from  two  to  three  feet  apart  from  centre  to 
centre.     This  thickness  of  plank  is  greater  than  is  required 
for  strength,  but  has  been  found  necessary  to  enable  the  road- 
way to  withstand  the  shocks,  friction,  and  wear  due  to  the 
travel  over  it. 

If  the  longitudinal  pieces  which  rest  directly  on  the  sup- 
ports are  too  far  apart  to  allow  the  plank  to  rest  safely  upon 
them,  cross  pieces,  called  roadway  bearers,  are  placed  upon 
the  longitudinal  pieces.  On  these  cross  pieces  other  longitu- 
dinal pieces,  called  joists,  are  placed  close  enough  together, 
and  the  planking  is  laid  upon  the  joists. 

The  particular  kind  and  width  of  roadway  will  depend 
upon  the  character  of  the  travel  over  the  bridge.  Knowing 
these,  the  weight  per  unit  of  length  is  quickly  determined. 

437.  Piers  and  abutments. — Walls  should   be   built  to 
support  the  ends  of  the  beams.     These  walls  may  be  of  stone, 
wood,  or  iron.     Those  placed  at  the  ends  of  the  bridge  are 


320  CIVIL   ENGINEERING. 

called  abutments  ;  the  intermediate  ones  are  termed  piers ; 
the  distance  or  space  between  any  two  consecutive  piers  is 
called  a  span,  and  sometimes  a  bay. 

If  the  frame  of  the  bridge  is  of  a  form  that  exerts  a  lateral 
thrust,  as,  for  instance,  in  an  arch,  the  abutments  and  piers 
must  be  proportioned  to  resist  this  thrust. 

As  the  foundations  are  exposed  to  the  action  of  currents 
of  water,  precaution  must  be  taken  to  secure  them  from  any 
damage  from  this  source.  The  piers  and  abutments  must  also 
be  guarded  against  shocks  from  heavy  bodies  and  against  the 
damaging  effects  of  floating  ice. 

438.  Wooden  piers  and  abutments. — Wooden  abutments 
may  be  constructed  of  crib-work.  The  crib  is  ordinarily 
formed  of  square  timber  or  logs  hewn  flat  on  two  of  their 
opposite  sides.  The  logs  are  halved  into  each  other  at  the 
angles,  are  fastened  together  by  bolts  or  pins,  and  are  some- 
times further  strengthened  by  diagonal  ties.  The  rectangular 
space  thus  enclosed  is  filled  with  earth  or  loose  stone.  V  ery 
frequently  the  crib  is  built  with  three  sides  only.  Another 
way  of  constructing  the  abutment  is  to  make  a  retaining  wall 
of  timber  by  which  the  earth  of  the  bank  is  held  up. 

The  piers  also  are  sometimes  made  of  cribs.  The  cribs  are 
floated  to  the  spot,  sunk  in  place,  filled  with  stone,  and  built 
up  to  the  proper  height.  There  are  serious  objections  to 
their  use  for  piers,  and  they  are  recommended  only  where  no 
injurious  results  will  follow  their  adoption,  and  where  it  is 
not  expedient  to  employ  some  one  of  the  other  methods. 

The  pier  made  of  piles  is  the  most  common  form  of  the 
wooden  pier.  It  is  constructed  by  driving  piles  from  three 
to  six  feet  apart,  in  a  row,  parallel  to  the  direction  of  the 
current.  The  piles  are  then  cut  off  at  the  proper  distance 
above  the  surface  of  the  water,  and  capped  with  a  heavy 
piece  of  square  timber.  If  the  piles  extend  some  distance 
above  the  water,  they  must  be  stiffened  by  diagonal  braces. 

In  some  cases  the  piles  are  cut  off,  at  or  just  below  the  level 
of  the  water,  so  that  the  capping  piece  will  always  be  kept 
wet.  Mortises  are  made  in  this  cap  into  which  uprights  are 
fitted  ;  the  uprights  taking  the  place  of  the  upper  parts  of  the 
piles  in  the  preceding  case.  Or,  what  is  more  common,  a 
trestle  made  in  the  form  of  an  inverted  W  is  fitted  on  this 
cap,  and  the  upper  side  of  this  trestle  is  capped  with  a  square 
piece  of  timber. 

Where  the  bottom  is  hard  and  not  liable  to  "  scour,"  the 
piles  are  dispensed  with  and  the  trestle  alone  is  used.  In 
this  case  the  piece  on  which  the  trestle  rests  is  laid  flat  on  the 


FENDERS   AND   ICE-BEE  AKER8. 


321 


bottom  and  is  called  the  mud-sill.  The  upper  part  of  the 
trestle  is  capped  as  before,  and  if  necessary  to  get  additional 
height  another  trestle  is  framed  on  top  of  this. 

439.  Fenders  and  ice-breakers. — Wooden  piers  are  not 
constructed  to  resist  heavy  shocks  from  floating  bodies.  In 
positions  exposed  to  such  shocks,  fenders  should  be  built.  A 
clump  of  piles  driven  on  the  exposed  side  of  the  pier,  oppo- 
site to  and  some  distance  from  it,  will  be  a  sufficient  protec- 
tion against  ordinary  floating  bodies  when  the  current  is 
gentle.  The  piles  should  be  bound  together  so  as  to  increase 
their  resistance;  this  may  be  done  by  wrapping  a  chain 
around  their  heads.  If  there  is  danger  from  floating  ice,  an 
inclined  beam  (Fig.  157),  protected  by  iron,  should  be  used 
to  break  up  the  ice  as  it  moves  towards  the  pier. 

Elevation. 


FIG.  157.     Plan. 


In  rapid  currents,  where  the  ice  is  thick,  a  crib-work 
square  in  plan,  with  one  of  the  angles  up-stream,  has  been 
used.  The  crib  was  filled  with  heavy  stone  and  the  up-stream 
angle  was  gjven  a  slope  and  was  protected  by  a  covering  of 
iron. 

The  construction  shown  in  Fig.  158  is  a  good  one.  Its  re- 
sisting power  is  increased  by  filling  the  interior  with  stone. 

440.  Masonry  piers  and  abutments. — The  methods, 
described  in  the  chapters  on  masonry  and  foundations,  are 
applicable  to  the  construction  of  piers  and  abutments. 

Since  they  are,  from  their  position,  especially  liable  to 
damage  from  the  action  of  currents,  both  on  the  soil  around 
them  and  on  the  materials  of  which  they  are  made,  particular 
attention  should  be  paid  to  their  construction. 
21 


322 


CIVIL   ENGINEERING. 


In  preparing  the  bed,  a  wide  footing  should  be  given 
to  the  foundation  courses,  if  the  soil  is  at  all  yielding,  and 
whenever  this  footing  does  not  rest  on  rock,  means  should  be 
taken  to  secure  the  bed  from  any  injurious  action  of  the 
water. 

Elevation. 


FIG.  158.    Plan. 


The  piers,  although  they  are  generally  built  with  a  slight 
batter,  may  be  built  vertical.  The  thickness  given  them  is 
greater  than  is  necessary  to  support  the  load  which  is  to  be 
placed  upon  them,  in  order  that  they  may  better  resist  the 
shocks  from  heavy  floating  bodies  and  the  action  of  the  cur- 
rents to  which  they  are  continually  exposed. 


FlG.  159. — A,  horizontal  sections  of  starling. 
B,  same  of  pier. 

They  should  be  placed,  if  possible,  so  that  their  longest 
dimensions  should  be  parallel  to  the  direction  of  the  current 
They  should  have  their  up  and  down-stream  faces  either 


FENDERS   AND   ICE-BREAKERS. 


323 


curved  or  pointed,  to  act  as  cut- waters  turning  the  current 
aside,  and  preventing  the  formation  of  whirls,  and  to  act  as 
fenders. 

These  curved  or  pointed  projections  are  called  starlings. 
Of  the  different  forms  of  horizontal  section  which  have  been 
given  them  (Fig.  159),  the  semi-ellipse  appears  to  be  the  most 
satisfactory. 

Their  vertical  outline  may  be  either  straight  or  slightly 
curved.  They  are  built  at  least  as  high  as  the  highest  water 
line,  and  finished  at  the  top  with  a  coping  stone  called  a 
hood. 

In  streams  subject  to  freshets  and  to  floating  ice,  the  up- 
stream starlings  are  provided  with  an  inclined  ridge  to 
facilitate  the  breaking  of  the  ice  as  it  floats  against  and  by 
them.  Where  very  large  masses  are  swept  against  the  piers, 


FIG.  160 — Represents  longitudinal  section,  elevation,  and  plan  of  a  piei 
of  the  Potomac  aqueduct  bridge. 

A,  A,  up-stream  starling,  with  the  inclined  ice-breaker  D,  which  rises  from 
the  low-water  level  above  that  of  the  highest  freshets. 

B,  down-stream  starling. 

E,  top  of  pier. 

F,  horizontal  projection  of  ice-breaker. 

it  is  not  unusual  to  detach  the  ice-breakers  and  place  them  in 
front  of  the  piers,  as  is  generally  done  in  the  case  of  wooden 
piers. 
Fig  160  represents  the  ice-breaker  planned  and  constructed 


324:  CIVIL  ENGINEERING. 

by  Colonel  Turnbull,  of  the  Topographical  Engineers,  United 
States  Army,  for  the  piers  of  the  Potomac  aqueduct  bridge 
of  the  Alexandria  Canal,  at  Georgetown,  D.  C. 

The  pier  was  at  the  bottom  66.6  feet  long  and  17.3  thick, 
and  terminated  by  starlings  whose  horizontal  cross-section 
was  circular.  The  pier  shown  in  the  drawing  was  61  feet 
high,  and  built  with  a  batter  of  ±f. 

The  starlings  were  built  up  with  the  same  batter,  except 
that  the  up-stream  one,  when  at  the  height  of  5  feet  below 
the  level  of  high  water,  received  an  inclination  of  45°,  which 
it  retained  until  10  feet  above  it.  From  there  to  the  top  it 
had  the  same  batter  as  the  rest  of  the  pier.  The  two  lower 
courses  of  the  ice-breaker  were  22  inches  thick,  the  rest  being 
18  inches.  The  stones  were  laid  in  cement,  and  no  stone  was 
allowed  in  the  ice-breaker  of  a  less  volume  than  20  cubic 
feet. 

The  ice  brought  down  by  the  river 'at  this  point  is  often  16 
inches  thick,  and  the  current  is  often  six  miles  an  hour.  On 
such  occasions  the  ice  is  forced  up  the  ice-breakers  to  a 
height  of  10  or  12  feet.  The  ice  breaks  by  its  own 
weight,  and  passes  off  between  the  piers  without  doing  any 
harm. 

Probably  the  ice-breakers  of  the  International  Bridge,  over 
the  Niagara  River,  at  Buffalo,  are  more  severely  tested  than 
any  in  our  country.  They  are  triangular  in  plan,  have  a 
slope  of  i,  and  are  protected  by  iron  plating. 

441.  Iron  piers  and  abutments. — Until  a  very  few  years 
ago  all  piers  were  made  either  of  masonry  or  timber.  Where 
a  solid  bed  could  not  be  reached  by  excavation,  piles  were 
driven,  their  tops  were  sawed  off,  and  on  them  a  grillage  and 
platform  was  placed  to  form  the  bed. 

The  substitution  of  iron  for  wood  in  many  engineering 
structures,  soon  led  to  the  use  of  iron  in  the  above  class  of 
constructions. 

Iron  is  used  in  the  construction  of  piers  and  abutments  in 
various  forms  as  follows : 

1.  As  piles  or  columns,  wholly  of  iron  ;  as  screw  piles. 

2.  As  a  hollow  column,  open  at  the  bottom,  and  partly  or 
entirely  filled  with  concrete ;  the  weight  of  the  bridge  resting 
on  the  iron  casing. 

3.  As  a  cylinder,  entirely  filled  with  masonry  or  concrete  ; 
the  weight  of  the  bridge  resting  on  the  masonry,  the  iron 
casing  serving  to  protect  and  to  stiffen  the  column. 

4.  As  a  caisson ;  the  sides  being  left  standing. 


APPROACHES. 


325 


The  precautions  recommended  for  stone  and  wooden  piers 
are  equally  necessary  for  those  made  of  iron. 

442.  Approaches. — The  portions  of  the  roadway,  at  each 
extremity  of  the  bridge  and  leading  to  it,  are  termed  the 
approaches. 

These  are  to  be  arranged  so  that  vehicles,  using  the  bridge, 
may  have  an  easy  and  safe  access  thereto. 

The  arrangement  will  depend  upon  the  locality,  upon  the 
number  and  direction  of  the  avenues  leading  to  the  bridge, 
upon  the  width  of  these  avenues  and  upon  their  position, 
whether  above  or  below  the  natural  surface  of  the  ground. 

When  the  avenue  to  the  bridge  is  in  the  same  line  as  its 
axis,  and  the  roadway  of  the  avenue  and  of  the  bridge  is  of 
the  same  width,  the  abutment  is  generally  made  as  shown  in 
Fig.  161.  The  returns  or  short  walls  carried  back  parallel  to 


FIG.  161. 


the  axis  of  the  road  to  flank  the  approach  are  called  wing- 
walls,  and  are  intended  to  sustain  the  embankment  as  well  as 
to  serve  as  a  counterfort  to  the  abutment. 


FIG.  162 — Represents  a  horizontal  section  of  an  abutment,  A,  with  curved  wing- 
walls,  B,  B,  connected  with  a  central  buttress,  C,  by  a  cross  tie-wall,  D. 

When  several  avenues  meet  at  the  bridge,  or  it  is  necessary 
that  the  width  of  the  approach  shall  be  greater  than  the 


326  CIVIL  ENGINEERING. 

way  of  the  bridge,  the  wing-walls  may  be  given  a  curved 
shape,  as  shown  in  Fig.  162,  in  this  way  widening  the 
approach. 

When  the  soil  of  the  river  banks  is  bad,  the  foundation  of 
the  wing-walls  should  be  laid  at  the  same  depth  as  that  of  the 
abutment.  But  if  the  soil  ^s  firm,  they  may  be  built  in  steps, 
and  thus  save  considerable  expense. 

The  rules  for  the  dimensions  of  wing- walls  are  the  same  as 
for  other  retaining  walls.  A  common  rule  is  to  make  their 
length  one  and  a  half  times  the  height  of  the  roadway  above 
the  bed  of  the  river,  their  thickness  at  bottom  one-fourth  their 
height,  and  to  build  them  up  in  off-sets  on  the  inside,  reduc- 
ing their  thickness  at  the  top  to  between  2  and  3  feet. 

In  some  cases  plane-faced  wing-walls  are  arranged  so  that 
the  faces  make  a  given  angle  with  the  head  of  the  bridge. 
The  top  of  the  wall  is  given  a  slope  to  suit  the  locality,  and 
is  covered  by  a  coping  of  flat  stones,  to  shelter  the  joints 
and  to  add  a  pleasing  appearance  to  the  wall  (Fig.  163). 
The  lower  end  of  the  coping  is  generally  terminated  by  a 
newel  stone. 


Instead  of  wing-walls,  a  single  wall  in  the  middle  is  used 
in  many  cases.  The  plan  of  the  abutment  in  such  a  case  is 
that  of  a  T. 

In  case  there  are  no  wing-walls  to  retain  the  earth,  the 
abutment  wall  must  be  sufficiently  distant  from  the  crest 
of  the  slope  of  the  water-course  to  allow  room  for  the  slope 
of  the  embankment.  This  slope  of  the  embankment  may  be 
the  natural  slope,  or,  if  steeper,  the  embankment  should  be 
revetted  with  dry  stone  or  sods,  as  shown  in  Fig.  164. 

It  may  be  necessary,  to  avoid  obstructing  the  communica- 


WATER   WINGS. 


327 


tions  along  the  bank,  to  construct  arched  passage-ways  under 
the  roadway  of  the  approaches. 


FIG.  164. — Plan  and  elevation  showing  a  method  of  arranging  the  em- 
bankments where  there  are  no  wing- walls, 
a,  a',  side  slopes  of  embankment  of  the  approach. 
6,  J',  dry  stone  revetment  of  the  slope  towards  the  water-course. 
d,  d',  dry  stone  facing  of  the  slope  of  the  bank, 
«,  «',  paving  used  on  the  bottom  of  stream. 
/,  /',  stairs  for  foot  passengers. 

443.  Water  wings. — When  the  face  of  the  abutment  pro- 
jects beyond  the  bank,  an  embankment  faced  with  stone  should 
connect  it  with  points  of  the  bank,  both  above  and  below  the 
bridge.    These  are  called  -water-wings,  and  serve  to  contract 
gradually  the  water-way  of  the  stream  at  this  point. 

Where  there  is  danger  of  the  banks  above  and  below  the 
abutment  being  washed  or  worn  away  by  the  action  of  the 
current,  it  is  advised  to  face  the  slope  of  the  bank  with  dry 
stone  or  masonry,  as  shown  in  Fig.  164. 

444.  The  frame. — It  is  evident  that  the  arrangement  used 
to  support  the  roadway  admits  of  the  greatest  differences  in 
form.    From  these  differences  in  the  forms  used,  many  classi- 
fications have  been  made. 


328  CIVIL   ENGINEERING. 

According  to  the  kind  of  frame,  bridges  may  for  analysis 
be  classed  as  follows : 

I.  Trussed  Bridges  j 

II.  Tubular  Bridges  j 

[II.  Arched  Bridges  •  and 

IY.  Suspension  Bridges. 

Considering  the  simple  bridge  to  belong  to  the  first  class, 
every  bridge  may  be  placed  under  the  head  of  one  or  more 
of  these  divisions. 


CHAPTER  XIY. 

L— TRUSSED  BRIDGES. 

445.  A  trussed  bridge  is  one  in  which  the  frame  support- 
ing the  roadway  is  an  open-built  beam  or  truss. 

A  truss  has  been  defined  (Art.  252)  to  be  a  frame  in  which 
two  beams  either  single  or  solid  built,  with  openings  between 
them,  are  connected  by  cross  and  diagonal  pieces  so  that  the 
whole  arrangement  acts  as  a  single  beam. 

It  generally  has  to  sustain  a  transverse  strain  caused  by  a 
weight  which  it  supports.  To  do  this  in  the  best  manner, 
the  axes  of  the  pieces  of  which  the  truss  is  composed  are  kept 
in  the  same  vertical  plane  with  the  axis  of  the  truss,  or  are 
symmetrically  disposed  with  reference  to  it. 

Supposing  the  truss  to  rest  on  two  or  more  points  of  sup- 
port, in  the  same  horizontal  line,  its  upper  and  lower  sides 
are  called  chords.  In  some  cases  the  upper  side  has  been 
called  a  straining  beam,  and  the  lower  a  tie.  Sometimes 
both  beams  are  designated  as  stringers.  English  writers  call 
them  booms. 

Generally,  both  chords  are  straight  and  parallel  to  each 
other.  Both  may  be  and  are  sometimes  curved  ;  in  some  cases 
one  is  curved  and  the  other  is  straight. 

The  secondary  pieces,  or  those  connecting  the  chords,  are 
called  braces,  and  are  so  arranged  as  to  divide  the  frame 
into  a  series  of  triangular  figures.  The  braces  are  known  as 
struts  or  ties,  depending  upon  the  kind  of  strain  they  have 
to  sustain.  The  triangles  may  be  scalene,  isosceles,  equila- 
teral, or  right  angled.  They  may  be  placed  so  as  to  form  a 
system  of  single  triangles,  or  by  overlapping,  form  a  lattice 
or  trellis  pattern. 


CALCULATING   THE   STRAIN   ON   A   TRUSS.  329 

446.  Systems. — Trussed  bridges  are  divided  into  three 
general  systems : 

1,  The  triangular  system ;  2,  The  panel  system  ;  3,  The 
bowstring  system. 

Other  subdivisions  are  frequently  made,  based  upon  the 
^articular  arrangement  adopted  for  the  braces  and  upon  the 
form  given  to  the  chords. 

Special  cases  belonging  to  the  systems  are  generally  known 
by  the  name  of  the  inventor:  as  Long's  truss,  Howe's, 
Fink's,  etc. 

The  essential  qualities  in  a  truss  are  those  already  given  for 
a  frame  (Art.  231),  viz.,  strength,  stiffness,  lightness,  and 
economy  of  material. 

These  qualities  are  dependent  upon  the  kind  of  material 
used  in  its  construction,  the  size  of  the  pieces,  and  the  method 
of  arranging  them  in  the  frame.  The  latter  gives  rise  to  the 
variety  of  trusses  met  with  in  practice. 


METHODS   OF   CALCULATING   STRAINS  ON  THE  DIFFERENT  PARTS  OF 

A  TRUSS. 

447.  External  forces  acting  on  a  truss. — It  is  necessary 
to  know  all  the  external  forces  which  act  on  a  truss,  in  order 
to  determine  the  strains  on  its  different  parts. 

The  external  forces  which  are  considered,  are : 

\ ,  The  weight  of  the  bridge ; 

2,  The  moving  or  live  load  ; 

3,  The  reactions  at  the  points  of  support ; 

4,  The  horizontal  and  twisting  forces  which  tend   to 
push  the  frame  in  a  lateral  direction  or  around  some  line  in 
the  direction  of  its  length. 

1.  The  weight  of  the  bridge. — Previous  to  the  calcula- 
tion of  the  strains,  the  weight  is  not  known,  since  it  is  de- 
pendent upon  the  thing  which  we  seek,  viz.,  the  dimensions 
of  the  parts  of  the  bridge.  An  approximate  weight  is  there- 
fore assumed,  being  taken  by  comparison  with  that  of  some 
similar  structure  already  built.  The  strains  are  then 
determined  under  the  supposition  that  this  is  the  weight 
of  the  bridge  and  the  dimensions  of  its  parts  are  computed. 
The  weight  is  then  calculated  from  these  dimensions,  and  if 
the  assumed  weight  does  not  exceed  very  greatly  that  of  the 
one  computed,  the  latter,  and  also  the  strains  deduced  there- 
from, are  assumed  to  be  correct. 


330  CIVIL  ENGINEERING. 

2.  The  moving  load. — This  is  any  load  which  may  pass 
over  the  bridge,  and  when  calculating  the  strains,  should  be 
assumed  at  its  maximum ;  that  is,  as  equal  to  or  exceeding 
slightly  the  greatest  load  which  will  ever  be  placed  on  the 
structure.  This  load  should  be  considered  as  occupying  vari- 
ous positions  on  the  bridge,  and  the  greatest  strains  in  these 
positions  determined. 

For  a  common  road  bridge,  the  load  is  assumed  to  be  a 
maximum  when  the  bridge  is  covered  completely  with  men. 
This  load  is  estimated  at  120  pounds  to  the  square  foot,  and 
must  be  added  to  the  weight  of  the  bridge. 

For  a  railroad  bridge,  the  load  is  assumed  a  maximum  when 
a  train  of  locomotives  extends  from  one  end  of  the  bridge  ta 
the  other.  This  load  is  assumed  at  one  ton  (2,240  Ibs.)  to  the 
running  foot. 

Sometimes,  common  road  bridges  are  liable  to  be  crossed 
by  elephants,  in  which  case  it  is  assumed  that  the  maximum 
load  is  equivalent  to  that  of  7,000  pounds  supported  on  two 
points,  six  feet  apart. 

A  load  applied  suddenly  produces  on  the  parts  of  a  bridge 
double  the  strain  which  the  same  load  would  produce  if  it 
were  applied  gradually,  beginning  at  zero  and  increasing 
gradually  until  the  whole  load  rested  on  the  bridge.  A  load 
moving  swiftly  on  the  bridge  approximates  in  its  effect  to 
that  of  one  applied  suddenly. 

Therefore,  the  action  of  a  live  load  may  be  considered  to 
be  the  same  as  that  of  a  load  of  double  its  weight  placed  care- 
fully on  the  bridge*  The  latter  may  then  be  treated  as  any 
stationary  load  added  to  the  weight  of  the  bridge ;  the  strains 
can  be  determined  in  the  usual  manner. 

To  distinguish  between  these  loads,  it  is  usual  to  call  the 
weight  of  the  bridge  the  permanent  or  dead  load,  and  that 
caused  by  bodies  crossing  the  bridge  the  moving,  the  rolling, 
or  the^live  load. 

3.  Reactions  of  the  points  of  support. — The  applied 
forces  cause  reactions  at  the  points  of  support,  which  must  be 
considered  in  the  calculations,  as  external  forces  acting  on 
the  bridge ;  their  value,  therefore,  must  be  determined.  No 
sensible  error  is  committed  by  regarding  the  reactions  as  verti- 
cal for  trusses  whose  chords  are  straight  and  parallel  to  each 
other. 

4  Forces  producing  lateral  displacement  or  twist- 
ing.— The  action  of  the  wind  on  the  sides  of  the  truss  tends 
to  push  the  bridge  in  a  horizontal  direction.  This  pressure 
may  be  regarded  as  uniform  over  the  entire  extent  of  the 


UNO-POST  TRUSS.  331 

surface  exposed.  The  best  authorities  assume  this  pressure 
ordinarily  at  forty  pounds  per  square  foot.  The  locality  will 
decide  as  to  the  exact  amount,  since  the  force  of  the  wind 
is  greater  in  one  place  than  in  another.  The  wind  gauge 
has  recorded  as  high  as  sixty  pounds  in  this  locality. 

Care  is  taken  to  guard  against  any  forces  which  might 
produce  a  twisting  strain,  and  to  reduce  their  effect  to  a  mini- 
mum. If  there  be  any  such  forces  acting,  their  effect  on  the 
bridge  must  be  provided  for. 


The  King-post  Truss. 

448.  Excepting  the  triangular  frame  (Art.  256),  the  king- 
post truss  is  the  simplest  of  the  trusses  belonging  to  the  tri- 
angular system. 

It  is  frequently  employed  in  bridges  of  short  span,  and 
where  the  span  is  so  small  that  the  beam  requires  support 
only  at  its  middle  point. 

For  a  single  roadway,  two  of  these  frames  are  placed  side 
by  side,  and  far  enough  apart  to  allow  room  for  the  roadway 
between  them.  Roadway  bearers  are  placed  on  the  beams, 
or  are  suspended  from  them,  to  support  the  joists  and  flooring. 
Each  truss  will  therefore  be  loaded  with  its  own  weight, 
one-half  that  of  the  roadway,  and  one-half  of  the  live  load. 
Knowing  these  weights,  the  strains  on  the  different  parts 
are  easily  determined,  and  the  dimensions  of  the  parts  cal- 
culated. 

To  determine  the  amount  and  kind  of  strains  on  the  parts, 
consider  the  load  resting  on  the  beams  as  uniformly  distri- 
buted over  them,  and  represent  (Fig.  68),  by  w,  the  load  on  a 
unit  of  length  of  the  beam,  C ;  2Z,  the  distance  between  the 
points  of  support. 

The  load  on  the  beam,  C,  will  be  %wl.  The  post,  <?,  is  so 
framed  upon  the  inclined  braces,  ere^  and  into  the  beam,  C, 
that  the  middle  point  of  the  beam  is  kept  in  the  same  straight 
line  with  its  ends.  C  is  therefore  in  the  condition  of  a  beam 
resting  on  three  points  of  support  in  a  light  line.  Five- 
eighths  of  the  load  2wl,  is  therefore  held  up  by  the  king-post 
(Art.  186),  and  by  it  transmitted  to  the  apex  of  the  frame, 
the  king-post  sustaining  a  tensile  stress.  The  amount  of  this 
stress  being  known,  the  dimensions  required  for  the  king-post 
are  easily  calculated. 

The  stresses  developed  and  the  dimensions  of  the  braces 
are  determined  as  in  Art.  256. 


332 


CIVIL    ENGINEERING. 


FIG.  165. 


If  the  middle  point  of  a  beam,  as  A  B  (Fig.  165),  is  sup- 
ported  at  C  by  inclined  braces  resting  against  the  abutments, 

the  amount  and  kind  of 
stresses  in  the  braces  are  the 
same  as  those  in  the  king-post 
truss;  in  this  case  the  hori- 
zontal thrust  at  the  lower 
ends  of  the  braces,  instead 
of  being  taken  up  by  a  tie 
beam,  will  act  directly  against 
the  abutments. 

Inverted  king-post.— If  the  king-post  truss  be  inverted, 

and  supported  at  the  extrem- 
ities (Fig.  166),  the  amount  of 
stress  in  each  piece  will  be 
the  same  as  before.  The 
strains,  however,  will  be  re- 
versed in  kind;  that  on  the 
beam,  and  that  on  the  king-post,  being  compression,  and  those 
on  the  braces  being  tension. 


FIG.  166. 


FINK  TRUSS. 

449.  Fink  truss. — This  is  the  name  by  which  a  truss  de- 
vised by  Mr.  Albert  Fink,  civil  engineer,  is  generally  known 
(Fig.  167).  It  consists  of  a  combination  of  inverted  king-post 
trusses,  as  shown  in  the  figure.  There  is  a  primary  truss, 
A  0  B  ;  two  secondary  ones,  A  K  C  and  C  L  B  ;  four  tertiary 
ones,  A  P  D,  D  M  C,  etc. 


M        0        N 
FIG  167. 

The  load  may  be  upon  the  upper  or  the  lower  chord,  as  the 
circumstances  may  require.  The  strains  on  the  different 
parts  are  easily  determined,  when  the  weights  to  be  placed 
upon  the  bridge  are  known. 

If  the  load  should  be  on  the  upper  chord,  there  would  be 
no  necessity  for  a  lower  chord,  so  far  as  strength  is  con- 
cerned. 

450.  Bollman  truss. — If  the  braces  all  pass  from  the  foot 


TRIANGULAB   TETT88. 


333 


of  the  posts  to  the  ends  of  the  chord,  as  in  Fig.  168,  the  truss 
thus  formed  is  known  as  Bollman's  truss. 


FIG.  168. 

The  calculations  for  the  strains  do  not  differ  in  principle 
from  those  in  the  preceding  case.  It  is  observed  that  the  ties 
are  of  unequal  length  in  each  of  the  triangular  frames  of  this 
truss ;  excepting  the  one  at  the  middle  post. 

There  is  no  necessity,  as  in  Fink's,  for  a  lower  chord  if  the 
load  is  placed  above  the  truss. 

From  the  fact  that  they  need  but  one  chord,  both  of  these 
constructions  are  frequently  called  "trussed  girders,"  to 
distinguish  them  from  the  ordinary  bridge-truss,  which,  by 
the  definition  given  for  a  truss,  requires  two  chords. 


I.  The  Triangular  System. 

451.  The  term,  triangular  truss,  is  ordinarily  used  to  de- 
signate a  truss  whose  chords  are  connected  by  inclined  braces, 
so  arranged  as  to  divide  the  space  between  them  into  isos- 
celes or  equilateral  triangles,  as  shown  in  Fig.  169. 


&— **i 


In  the  isosceles  bracing  the  braces  are  generally  arranged 
so  as  to  make  an  angle  of  forty-five  degrees  with  the  vertical, 
although  sometimes  other  angles  are  used. 

When  the  triangles  are  equilateral,  the  truss  is  known  in 
England  and  in  the  United  States  as  the  "  Warren  girder," 
and  in  other  countries  as  the  "  Neville." 

The  strains  on  this  truss  may  be  determined  by  the  methods 
given  in  Arts.  260-1-2,  or  they  may  be  determined  by  using 
the  reactions  of  the  points  of  support  when  these  reactions  are 
known.  The  following  is  an  example  of  the  latter  method. 


334  CIVIL   ENGINEERING. 

452.  Let  it  be  required  to  determine  the  strains  produced 
upon  the  different  parts  of  a  triangular  truss  by  a  weight 
supported  at  the  middle  point  of  the  truss. 

The  truss  is  supposed  to  be  resting  on  firm  points  of  sup 
port  at  its  ends,  these  supports  being  in  the  same  horizontal 
line. 

Eepresent  by  (Fig.  169), 

2W,  the  weight  resting  on  the  truss  at  the  middle ; 

K!  ES,  the  reactions  at  the  points  of  support ; 

a,  the  angle  RI  At  Bt  between  the  brace  and  a  vertical  line. 

Since  the  load  is  at  the  middle,  the  reactions  due  to  it  are 
Ei  =  W,  and  E,  =  W1. 

The  strains  in  one  half  will  be  equal  to  the  corresponding 
strains  in  the  other  half.  Take  the  right  half,  as  shown  in  the 
figure,  and  on  Rt  =  W,  as  a  resultant,  construct  a  parallelo- 
gram of  forces,  the  components  of  which  are  in  the  directions 
of  the  pieces,  At  Bj  and  At  A3.  These  components  will  be 

Ty 

respectively  equal  to and  W  tan  a.     Going  to  B,,  and  re- 
cos  a 

solving into  two  components,  one  in  the  direction  of 

cos  a 
Bl  B,,  and   the  other  in  the  direction  of  B,  Aa,  their  values 

will  be  2W  tan  a  and Performing  the  same  operation 

cos  a 
at  A,,  for  the  components  in  the  directions  of  AQ  A3  and  Aa 

Ba,  there  are  found  the  same  values  just  determined,  2W  tan  a 

Ty 
and    —      At  B2,  A8,  B8,  etc.,  until  the  point  of  application 

cos  a 

of  the  force  is  reached,  similar  expressions  for  the  stresses  will 
be  found. 

Hence  the  stress  in  Bj  B2  is  equal  to  2W  tan  a  ;  in  B2  B8, 
this  same  amount  is  increased  by  that  in  Bj  B2,  or  4W  tan  a 
for  the  stress  in  B2  B3 ;  on  Bs  B4,  6W  tan  <*.,  etc.  The  stress 
in  A!  A2  is  W  tan  a ;  in  A2  A3,  it  is  2W  tan  a  increased  by 
that  in  Aj  A2,  or  in  all,  3W  tan  a;  in  A8  A4,  5W  tan  «,  etc. 

There  is  no  increase  of  the  stress  as  we  pass  from  one  brace 

W 

to  another,  the  intensity  being  the  same  for  each,  viz., . 

An  examination  of  the  forces  acting  will  show  the 
nature  of  the  strain  in  each  piece.  The  direction  of  the 
component  of  the  reaction  along  the  axis  of  the  chord  is 
towards  its  centre  or  middle  point ;  the  strain  is  therefore 
one  of  compression,  and  increases  from  each  end  toward  the 
middle. 


DETERMINING   THE    STRAIN. 

On  the  lower  chord,  the  strain  is  in  the  opposite  direction, 
and  is  therefore  tensile,  increasing  in  amount  towards  the 
centre,  as  already  shown. 

In  the  right  half  of  the  truss,  the  strain  on  the  brace  Aj  Bj 
and  on  those  parallel  to  it,  is  compress! ve ;  on  those  not  par 
allel  to  it,  the  strain  is  tensile. 

The  pieces  of  the  other  half  are  strained  in  a  similar  man- 
ner; on  the  corresponding  pieces,  the  strains  are  equal  in 
amount,  and  they  are  also  of  the  same  kind  on  the  braces, 
being  tensile  in  those  parallel  to  the  brace  ^  B1?  and  com- 
pressive  in  the  others. 

It  will  be  noticed  that  these  results  are  identical  with  those 
already  obtained  in  Art.  260. 

In  the  above  example,  the  load  was  placed  at  the  middle 
point  of  the  truss,  but  if  the  load  had  been  placed  at  any  other 
point,  the  process  used  to  obtain  the  strains  would  be  the  same ; 
it  would  only  be  necessary  to  find  the  corresponding  values  for 
R!  and  Rj,  and  substitute  them  in  the  foregoing  expressions. 

453.  Let  it  be  required,  to  determine  the  strains  produced 
upon  the  parts  of  this  truss  by  a  uniform  load  distributed 
over  the  lower  chord. 

The  effect  of  the  uniform  load  upon  the  truss  may,  without 
material  error,  be  considered  to  be  the  same  as  that  produced 
by  a  series  of  weights  acting  at  the  points  A1}  Ag,  A3,  A4, 
etc.,  each  weight  being  equal  to  that  part  of  the  uniform 
load  resting  on  the  adjacent  half  segments. 

Denote  by  n  the  number  of  these  points  thus  loaded,  and 
by  2w,  the  load  at  each  point. 

Their  total  weight  on  the  chord  will  be  2nw,  and  the 
reactions  at  the  points  of  support  due  to  them  will  be,  at  each 
support,  equal  to  nw. 

To  determine  the  strains,  proceed  as  before.  Construct 
the  parallelogram  on  R!  =nw,  and  determine  the  stresses  in 

A!  Ao  and  Aj  Bj,  which  are  found  to  be  nw  tan  or,  and  nW  . 

cos  OL 

Going  to  Bj,  the  stress  in  B1  B2  is  %nw  tan  ar,  and  that  in 
B!  AS  is  -  — .  At  Ag  the  components  of  2w,  acting  at  this 

point  in  the  direction  of  Ag  As  and  A2  B2  must  be  subtracted 
from  those  of  the  transmitted  forces  along  these  lines.  The 
stress  in  Ag  A3  will  therefore  be  %nw  tan  a  —  %w  tan  a  = 
2  (n— 1)  w  tan  a.  To  this  must  be  added  the  stress  already 
determined  in  At  A2,  which  gives  the  total  stress  in  AS  Ag  to 
be  w  [n  +  2  (n  —  1)  ]  tan  a. 


336  CIVIL   ENGINEERING. 

The  stress  in  A2  B2  is ,  which  may  be  written 

cos  a.       cos  a 

'  W.     Going  to  B2  the  stress  in  B2  B3,  produced  by  the 

COS  OL 

strain  on  the  brace  A2  B2,  is  2(n— 2)  w  tan  #,  to  which  the 
stress  in  Bj  B2  is  to  be  added,  making  the  total  stress  2 (n—2)w 
tan  a  +  2nw  tan  <*,  which  may  be  written  4(^—1)  w 
tan  a.  The  stress  in  B8  Aj  is  the  same  as  that  in  A2  B2, 

(n  —  %\w 

or  is  equal  to — . 

cos  a 

It  is  plain  that  the  stress  in  any  segment  of  the  upper 
chord  is  obtained  by  adding  to  the  stress  transmitted  to  it  by 
the  brace  with  which  it  is  connected,  the  respective  stresses  in 
each  of  the  segments  preceding  it ;  and,  that  the  same  law 
obtains  for  the  stresses  in  the  lower  chord. 

It  is  to  be  noticed  that  the  stresses  in  the  first  pair  of  braces 
are  the  same  in  intensity  but  different  in  kind,  being  compres- 
sive  for  the  first  and  tensile  for  the  second,  as  in  the  last  case ; 
that  in  the  next  pair  the  intensity  differs  from  that  in  the 

first  by ;  that  the  stresses  in  the  third  pair  differ  from 

J  cos  <*' 

the  second  by  the  same  quantity  ;  and  hence,  that  the  stress 
in  any  pair  may  be  obtained  when  that  in  the  preceding  one 

Qw 

is  known  by  subtracting from  it.  It  is  noticed  that  those 

tocos  a 

braces  whose  tops  incline  towards  the  middle  point  of  the 
truss  are  compressed,  while  those  that  incline  from  it  are 
extended. 

It  is  seen  that  while  the  strains  on  the  braces  decrease  from 
the  ends  towards  the  middle,  that  it  is  the  reverse  for  the 
chords ;  in  both  the  upper  and  lower,  the  strains  increase 
from  the  ends  to  the  middle. 

The  stresses  thus  determined  may  now  be  written  out,  as 
follows : 

1.  The  compressions  on  the  braces,  Aj  B,,  A2  B2,  A8  B8,  etc., 
are 

nw     (n  —  %)w   (n  —  4)  w   (n  —  6)w 

cos  a'      cos  a    '      cos  a     '       cos  a     ' 

2.  The  tensions  on  the  braces,  B!  A2,  B2  A8,  B}  A4,  etc.,  are 
the  same  in  amount,  viz., 

nw     (n  —  2)  w   (n  —  4:)  w 

j L—   _ 7      etc. 

coso-'       cos  a  cos  a     ' 


DETERMINING   THE   STRAIN.  337 

3.  The  compressions  on  the  segments  of  the  upper  chord 
are,  for  Bx  B2,  B2  B3,  B3  B4,  etc., 

%nw  tan  a,  ±(n  —l)w  tan  a,  6(71  —  2)  w  tan  a,  8(n  —  3)w  tan  a, 

etc. 

4.  The  tensions  on  the  segments  of  the  lower  chord  are,  for 
AI  A2,  Aj  A3,  As  A4,  etc., 

nw  tan  a,  [n  +  2  (n  —  1)]  w  tan  a,  [7i+4  (TI  —  2)  w  tan  a, 
[n-f  6  (n  —  3)  ]  w  tan  a,  etc. 

General  term.  —  By  examining  the  expressions  just  ob- 
tained for  compression  on  the  segments  of  the  upper  chord, 
it  is  seen  that  a  general  term  may  be  formed,  from  which  any 
one  of  these  may  be  deduced  upon  making  the  proper  substi- 
tution. Let  the  segments  be  numbered  from  the  ends  to  the 
middle,  by  the  consecutive  whole  numbers,  1,  2,  3,  4,  etc., 
and  represent  the  number  of  any  segment  by  m.  Then, 

2m  (n  —  m  +  1)  w  tan  a, 

will  be  the  general  term  expressing  the  intensity  of  the 
stress  in  the  n^  segment. 
It  is  seen  that  the  term, 

[n  +  2  (m  —  1)  (n  —  m  +  1)]  w  tan  a, 

will  represent  the  amount  of  tension  on  the  rath  segment  oi 
the  lower  chord. 

The  value  of  m  =  —  -  —  ,  corresponds  to  a  maximum  in  the 


first  expression,  and  upon  substitution  gives  ^(/i-fl)8  w  tan  a  for 
the  maximum  compression.  The  value  of  m  =  —  ~—  ,  corre- 

sponds to  a  maximum  in  the  second,  and  upon  being  substi- 
tituted  in  it  gives  £[  (n  +  I)2  —  1]  w  tan  a  for  the  maximum 
tension.  The  quantity,  n  +  1,  denotes  the  number  of  bays  in 
the  lower  chord,  which  if  we  represent  by  X,  the  expression, 

£N~2  w  tan  a, 

will  very  nearly  correspond  to  the  maximum  tension  or  com- 
pression upon  the  chords. 

Strains  on  the  chords.  —  The  strains  on  the  chords  vary  from 
segment  to  segment,  but  are  uniform  throughout  any  one  seg- 
ment. If  the  segments  were  infinitely  short,  the  strains  in  that 
case  would  be  a  continuous  function  of  the  abscissa,  and  the  rate 
of  increase  could  be  represented  by  the  ordinates  of  a 
parabola.  Suppose  a  vertical  section  made,  cutting  the  truss 
between  A4  and  B4,  and  A.  taken  as  the  centre  of  moments. 
22 


338 


CIVIL   ENGINEERING. 


From  the  principle  of  moments,  there  must  be  for  equilib- 
rium, 

d  x  d  =  \wv?  —  R!  a;, 
or 

wx2  —  2E,  x 
Cl  =         ~2d > 

in  which  x  is  the  distance  of  the  centre  of  moments  from  A!  ; 
Cj  is  the  stress  in  the  upper  piece  B3  B4 ;  d  the  distance  be- 
tween the  axes  of  the  chords ;  w  the  uniform  load  on  the 
unit  of  length ;  and  Bj  the  reaction  at  the  point  of  support 
A!.  This  is  the  equation  of  a  parabola  whose  axis  is  vertical 
and  whose  vertex  is  over  the  middle  of  the  truss. 

Remark. — The  usual  method  of  computing  the  strains 
upon  the  pieces  of  a  truss  is  that  of  adding  and  subtracting  for 
each  consecutive  piece,  as  shown  in  the  previous  methods  for 
calculating  strains.  General  formulas  are  used  in  connection 
with  these  methods  to  check  the  accuracy  of  the  computa- 
tions. 


II.  The  Panel  System. 

454.  If  the  ties  of  the  triangular  truss  be  pushed  around 
until  they  are  vertical,  we  shall  have  the  method  of  vertical 
and  diagonal  bracing  referred  to  in  Article  263,  and  the  re- 
sulting truss  will  be  a  type  of  the  system.  In  England  this 
truss  is  frequently  called  the  trellis  girder,  and  in  France 
the  American  "beam.  (Fig.  170.) 

BS  Bs  04  Bj  D9  B I 


\ 


As 


A* 

170. 


A3 


A2 


The  methods  already  given  for  the  determination  of  the 
strains  on  the  parts  of  a  Warren  truss,  and  on  a  frame  where 
vertical  and  diagonal  bracing  is  used,  can  be  applied  to  this 
truss. 

The  space  included  between  any  two  consecutive  verticals 
is  known  as  a  panel ;  hence  the  name  of  the  system. 

Diagonal  pieces,  as  shown  by  the  dotted  lines  in  the  figure, 


THE   QUEEN-POST. 


339 


called  counter-braces,  are  generally  inserted  in  each  panel. 
Their  particular  use  will  be  alluded  to  in  another  article. 


The  Queen-post^  or  Trapezoidal  Truss. 

455.  This  is  the  simplest  truss  belonging  to  the  panel  sys- 
tem, and  is  much  used  in  bridges  where  the  span  is  not  greater 
than  forty  or  fifty  feet.  Its  parts  are  most  strained  when 
the  load  extends  entirely  from  one  end  to  the  other.  Suppose 
this  load  to  be  uniformly  distributed  over  the  lower  chord, 
A!  A4,  and  represent  by  (Fig.  171), 

Z,  the  length  of  the  segment  At  A2 ; 

w,  the  weight  on  the  unit  of  length ;  and  by 

o,  the  angle  of  F^  A!  Bj. 


B> 


FIG.  171. 


Since  the  segments  Aj  A2,  A2  A8,  A3  A4,  are  ordinarily  equal 
to  each  other,  31  will  be  the  length  of  the  lower  chord,  and 
3wl  will  be  the  total  load  on  the  truss.  The  queen-posts  are 
framed  into  the  lower  chord ;  the  latter,  therefore,  has  four 
points  of  support.  Supposing  the  lower  chord  to  be  a  single 
beam,  or  so  connected  as  to  act  like  one  piece,  each  post 
would  sustain  J-J-  of  wl.  Each  weight  is  transmitted  to  the 
upper  end  of  its  post,  where  it  is  held  in  equilibrium  by  two 
forces,  one  acting  in  the  direction  of  the  inclined  brace,  and 
the  other  in  the  direction  of  the  chord  Bx  B2.  The  components 

along  Bt  At  and  B2  A4  are  each  equal  to  -fj  -    —  and  those 

COS  ft, 

along  Bx  B2  are  equal  to  fj-  wl  tan  a.  The  two  latter  balance 
each  other,  producing  a  strain  of  compression  on  the  upper 
chord.  The  other  two  produce  compression  on  the  braces, 
which,  transmitted  to  the  points  of  support,  causes  a  strain  of 
tension  on  the  lower  chord  and  a  vertical  pressure  on  the 
points  of  support.  Knowing  the  amount  and  kind  of  strains, 
the  dimensions  of  the  pieces  can  be  calculated. 

Instead  of  considering  the  lower  chord  as  a  beam  resting  on 
four  points  of  support,  it  is  more  usual  to  consider  that  one- 


340  CIVIL  ENGINEERING. 

third  of  the  entire  load  is  held  up  by  each  post,  and  one-sixth 
at  each  point  of  support  at  the  ends ;  or,  if  the  segments  are 
unequal  in  length,  to  consider  the  weight  held  up  by  each 
post  to  have  the  same  proportion  to  the  whole  load  that  the 
segments  have  to  the  entire  length  of  the  chord  Ax  A4.  The 
remarks  made  upon  the  inverted  king-post  truss  will  apply 
to  this  frame,  if  inverted. 

The  queen-post  truss,  in  its  present  shape,  will  not  change 
its  form  under  the  action  of  a  load  uniformly  distributed  over 
it;  when  loaded  in  this  manner,  the  truss  is  said  to  be 
balanced.  If,  however,  the  load  be  only  partially  distributed 
over  it,  so  that  the  resultant  acts  through  some  other  point 
than  the  middle  of  the  truss,  the  truss  may  become  distorted 
by  a  change  of  figure  in  the  parallelogram  A2B1B2A3.  The 
truss  is  then  said  to  be  unbalanced. 

Sometimes,  a  certain  amount  of  stiffness  in  the  joints  and 
of  resistance  to  bending  in  the  pieces,  give  sufficient  rigidity 
to  the  truss,  and  may  be  relied  upon  to  prevent  distortion 
under  light  loads. 

As  the  load  moves  from  one  point  to  another,  a  change  of 
form  will  generally  take  place,  due  to  the  elasticity  of  the 
materials  of  which  the  frame  is  made  and  to  the  imperfection 
of  the  joints.  To  prevent  this  change  of  form,  diagonal 
pieces  are  inserted,  as  shown  in  the  dotted  lines  of  the  figure. 
The  truss  is  then  said  to  be  thoroughly  braced. 

A  truss  is  said  to  be  thoroughly  braced  when  the  parts  are 
so  arranged  that  no  distortion  takes  place  under  the  action  of 
its  usual  load,  whatever  may  be  the  position  of  the  load. 

A  truss  may  be  distorted  and  even  broken,  by  an  excessive 
load,  notwithstanding  the  use  of  braces,  but  this  distortion  is 
excluded  by  the  definition  of  a  frame,  given  in  Art.  230. 

In  the  calculations  to  determine  the  strains,  the  joints  of 
the  truss  are  considered  to  be  perfect. 


III.  The  Bowstring  System. 

456,  The  common  bowstring  girder  is  one  in  which  the 
upper  chord  is  curved  into  either  a  circular  or  parabolic  form  and 
lias  its  ends  secured  to  the  lower  chord,  which  is  straight  (Fig. 
107).  The  horizontal  thrust  of  the  upper  beam  is  received  by  the 
lower  chord  ;  the  latter  therefore  acts  as  a  tie,  and  as  a  conse- 
quence, the  reactions  at  the  points  of  support  are  vertical.  The 
intermediate  space  between  the  bow  and  the  string  is  filled  with 


BOWSTRING    GIRDERS. 


341 


a  diagonal  bracing,  like  that  used  in  the  triangular  or  panel 
systems,  for  the  purpose  of  stiffening  the  truss. 

The  load  straining  the  girder  may  rest  directly  upon 
the  lower  chord  or  be  suspended  by  vertical  ties  from  the 
upper  one,  and  the  greatest  stresses  developed  in  the  pieces 
of  the  girder  are  found  by  the  usual  methods. 

"Where  the  span  is  of  considerable  length,  the  usual  practice 
is  to  form  the  upper  chord  of  a  number  of  straight  pieces, 
the  intersections  of  whose  axes  ace  in  the  curve  of  the  bow. 
(Fig.  172.) 


/?/ 


& 


As        A*       As        A2 
FIG.  172. 


To  find  the  strains  produced  upon  the  parts  of  a  truss  be- 
longing to  this  system,  by  a  uniform  load  resting  on  the  lower 
chord,  which  is  connected  with  the  upper  one  by  vertical  ties 
dividing  the  truss  into  an  even  number  of  panels  of  equal 
horizontal  length,  represent  by 

2#,  the  length  of  the  lower  chord  ; 

jf,  the  rise  of  the  curve,  or  depth  of  the  truss  at  the  centre  ; 

w,  the  weight  on  the  unit  of  length  of  the  lower  chord  ; 

Pj,  the  stress  in  any  piece  of  the  upper  chord  ;  and 

T!,  the  stress  in  the  lower  chord. 

Take  the  origin  of  the  co-ordinates  at  Ax,  the  axis  of  X  coin- 
ciding with  the  axis  of  the  lower  chord,  and  Y  perpendicu- 
lar to  it. 

Disregarding  the  braces,  and  supposing  a  vertical  section 
made  on  the  left  of  A3,  and  very  near  to  it,  and  B8  taken  as 
the  centre  of  moments. 

Taking  the  moments  around  this  point,  there  results 


=  K1aJ-         =        (2a-aJ;,    (155) 


aj,  representing  the  distance 

Taking  the  curve  containing  the  intersections  BU  B2,  B3,  etc., 
to  be  a  parabola,  its  general  equation  when  referred  to  the 
vertex  and  tangent  at  that  point  is 


34-2  CIVIL  ENGINEERING. 

The  vertex  being  the  origin,    the  value  of  y  —f  gives 
x  =  ±  #,  or 

whence, 


which  being  substituted  for  2p  in  the  equation  of  the  para« 
bola,  gives 

*  =  ^y,ory=4#,  .     .     .   (156) 
/  a 

Placing  the  origin  at  A1?  the  equation  of  the  curve  will 
be 

y  =  £(9o»-afy    .    .    .     (157) 

Since  A8B3  is  equal  to  y,  for  the  value  of  x  equal  to  A1A3, 
there  follows  from  the  substitution  of  this  value  of  A3B3,  in 
equation  (155), 

wx  (20  -  x)      via? 

Tl=T-^T-  =  a/'   '   •  (158) 

Hence,  the  strain  on  the  lower  chord,  produced  by  a  uni- 
form load,  is  constant  throughout. 

It  is  observed  that  this  is  the  same  value  obtained  for  the 
horizontal  component  of  the  thrust  in  Art.  228. 

In  the  same  section,  taking  the  moments  around  A3,  the 
lever  arm  of  the  strain  on  B2B8,  is  Asm  drawn  perpendicular 
to  the  piece  and.  through  the  centre  of  moments. 

There  results 

Pt  x  A3m  =  ~(2a  -  x).    .     .     (159) 
2 

Through  B2,  draw  a  straight  line  parallel  to  the  lower 
chord.  From  the  triangles  B2B8j?  and  A3B8m,  we  have  the 
proportion, 


The  first  term  of  this  proportion  is  the  length  of  the  piece 
of  the  upper  chord  in  this  panel,  and  varies  in  length  for  each 
panel  from  At  to  the  centre.  The  second  term  is  the  hori- 
zontal length  of  the  panel  and  constant.  Representing  the 
former  by  v,  and  the  latter  by  Z,  and  substituting  in  the  above 
proportion,  we  obtain 

I 

v  :  I : :  y  :  h*in.    .*.  Asm  =  v  — , 

9  v 


BOWSTRING   GIRDERS.  343 


a  v 

Substituting  which  in  equation  (159),  we  get 


<160> 


This  shows  that  the  strain  is  independent  of  x  and  depend- 
ent upon  v  the  only  variable  present,  and  that  it  increases  as 
v  increases,  or  is  greatest  at  the  points  of  support. 

Suppose  a  brace  to  be  inserted  in  this  panel,  joining  Aj 
and  B3,  or  B2  and  Ag.  A  section  taken  midway  between  A2 
and  Ag  would  cut  the  upper  chord,  the  lower,  and  the  brace. 
For  an  equilibrium,  the  algebraic  sum  of  the  horizontal  com- 
ponents and  of  the  vertical  components  of  all  the  forces  must 
oe  separately  equal  to  zero. 

Represent  the  strain  on  the  brace  by  F,  and  the  angles 
made  by  the  brace  and  the  piece  B2  B8  of  the  upper  chord 
with  a  vertical,  by  a  and  y3,  respectively. 

The  first  of  these  conditions  of  equilibrium  can  be  ex- 
pressed analytically,  as  follows  : 

P!  sin  0  -  F  sin  a  —  T  =  0. 

But  P!  sin  0  =  T  =  ^  ^,  hence 

2J 
F  sin  a  =  0,    or  F  =  0. 

That  is,  there  is  no  strain  on  the  brace  produced  by  a  load 
uniformly  distributed  over  the  truss. 

If  the  load  had  been  placed  directly  upon  the  upper  chord, 
there  would  have  been  no  strain  on  the  verticals. 

If  the  triangular  instead  of  the  panel  system  had  been 
used  for  the  bracing,  its  use  would  have  been  simply  to  trans- 
mit the  loads  on  the  lower  to  the  upper  chord.  Knowing 
the  angle  of  the  bracing,  the  strain  on  any  brace  could  be 
easily  determined. 

The  vertical  component  of  Pi  may  be  obtained  as  follows  : 

Let  y'  and  y"  be  the  ordiuates  of  the  lower  and  upper  ex- 
tremities of  any  piece,  as  B2  B8,  of  the  upper  chord. 

Let  v,  the  length  of  the  piece,  denote  the  intensity  of  the 
strain  on  the  piece,  then  y"  —  y'  would  represent  its  vertical 
component. 

From  the  equation  of  the  curve,  we  have 

y"  =  £  «"  (2a  -  a"),  and  y'  =  £«f  (20  -  a/> 


844  CIVIL   ENGINEERING. 

But  »"  =  xf  +  I,  substituting  which  in  the  first  of  these 
equations  for  x",  and  then  from  this  result  subtracting  the 
second  of  the  equations,  we  get 

y"  -y'  =f-±Va-W-l). 

Eepresenting  the  vertical  component  by  Y,  we  may  form 
the  following  proportion : 

v:y"  -  y'  ::  Pt :  Y. 

Substituting  for  Pt  and  y"  —  y' ,  the  values  just  found,  and 
solving,  we  find 

w 
V  =  2  (2a  -  <M  -  I),    .    .    (161) 

for  the  vertical  component. 


Other  Forms  of  Bowstring  Girders. 

457.  The  common  bowstring  girder  has  been  used  in  an 
inverted  position  by  simply  turning  it  over,  so  that  the  bow 
was   below  and  the  straight  chord   above.     This   inversion 
causes  no  difference  in  principle,  the  amount  of  strains  on 
the  different  parts  remains  the  same  as  before ;  the  kinds  of 
strains  are  changed,  being  compression  on  the  straight  chord 
and  tension  on  the  lower  one. 

By  combining  this  inverted  with  the  other  truss,  that  is, 
by  making  both  the  upper  and  lower  chords  curved,  another 
form  is  obtained.  This  arrangement  was  used  by  Brunei  in 
the  Saltash  Bridge. 

Where  the  amount  of  material  forms  an  important  item, 
both  in  the  weight  arid  cost  of  the  structure,  as  in  the  case  of 
very  large  spans,  the  last  form  can  be  more  advantageously 
used  than  any  of  the  other  forms  of  bowstring  girders. 

The  great  objection  to  the  bowstring.girder,  compared  with 
the  trusses  of  the  other  systems,  is  the  inferior  facilities  it 
affords  for  lateral  bracing. 

Compound  Systems. 

458.  If  two  or   more  of  the   trusses   already   described 
be    combined,  there    is    formed    a  class   known   as    com- 
pound trusses.     This  term  is  sometimes  limited  to  a  com- 


COMPOUND   SYSTEMS.  345 

bination  made  of  two  or  more  of  different  systems,  partic- 
ular names  being  given  to  those  made  of  the  same  system. 

As  they  can  be  always  resolved  into  their  simple  parts, 
there  is  no  need  of  a  separate  classification  except  for  des- 
criptive purposes. 

459.  Lattice  truss. — If  the  segments  of  the  simple  trian- 
gular bridge  truss  (Fig.  169)  be  bisected,  and  braces  inserted 
in  the  intervals  thus  formed  parallel  to  the  braces  already 
used,  a  truss  similar  to  that  shown  in  the  Fig.  173  is  formed. 


FIG.  173. 

The  dotted  lines  show  the  intermediate  braces.  This  ia 
called  a  double  triangular  truss,  although  sometimes  it  is 
known  as  the  half-lattice. 

By  dividing  the  segments  into  three,  four,  or  more  equal 
parts,  and  inserting  a  corresponding  number  of  braces,  the 
triple,  quadruple,  etc.,  triangular  trusses  are  formed.  They 
are  generally  known  as  lattice  trusses,  or  girders. 

To  determine  the  strains  on  a  truss  of  this  kind,  it  is  usual 
to  consider  the  truss  as  composed  of  two,  three,  four,  or  more 
simple  triangular  trusses,  as  the  case  may  be,  and  find  the 
strains  on  each  one  separately.  These  are  then  added  and 
the  strength  of  the  truss  considered  as  that  of  the  whole  com- 
bined. Under  this  supposition,  the  braces  are  regarded  as 
separate  from  each  other,  and  only  fastened  at  tEeir  ends. 
In  fact,  they  are  generally  fastened  together  at  their  inter- 
sections, which  adds  to  the  strength  of  the  combination  but 
complicates  the  problem  of  finding  the  amount  of  strain  on 
each  piece. 

A  subdivision  of  a  truss  of  the  panel  system,  and  putting 
in  another  set  of  panels  of  the  same  size,  will  give  a  compound 
truss  which  has  been  much  used.  A  calculation  of  the 
strains  is  made  in  the  same  way  as  that  just  described. 

Strains  Produced  by  a  Moving  Load. 

460.  Loads  placed  in  particular  positions,  or  stationary  loads, 
have  been  the  only  forces  considered  in  the  previous  examples. 
As  a  bridge  affords  continuous  roadway  between  two  points, 


346  CIVIL   ENGINEEEING. 

it  is  subjected  to  strains  produced  by  loads  which  move  over 
it,  and  it  is  essential  that  the  action  of  the  moving  loads  on 
the  parts  of  the  bridge  be  known. 

With  the  exception  of  the  shearing  strain,  it  has  already 
been  shown  that  the  strains  produced  by  a  moving  load  are 
the  greatest  when  the  centre  of  the  load  is  at  the  centre  of 
the  bridge,  and  will  be  at  the  maximum  when  the  moving 
load  covers  the  entire  structure. 

If,  then,  the  maximum  moving  load  that  will  ever  come 
upon  the  bridge  be  supposed  to  have  its  centre  at  the  middle 
of  the  bridge,  and  the  parts  of  the  bridge  determined  under 
this  supposition,  the  bridge  will  possess  the  requisite  strength. 

When  the  shearing  strain  enters  as  an  important  element, 
its  maximum  value  should  be  obtained,  and  the  parts  of  the 
bridge  proportioned  accordingly. 

461.  Counter-braces. — The  dotted  lines  in  Fig.  170  repre- 
sent pieces  of  the  truss  known  as  counter-braces.  If  the  truss 
supports  only  a  load  at  the  middle  point,  or  a  load  uniformly 
distributed  over  the  entire  truss,  these  counter-braces  are  not 
necessary.  In  ordinary  trusses  they  are  needed  to  resist  the 
action  of  moving  loads. 

Take  the  simple  triangular  bridge  truss,  and  suppose  it 
strained  by  a  live  load  which  is  uniformly  distributed  over 
the  lower  chord.  Let  this  live  load  extend  from  either  end 
of  the  truss  and  for  a  distance  equal  to  one-fourth  of  the  span. 
The  resultant  of  the  load  acts  through  its  middle  point,  which 
is  at  a  distance  from  the  end  of  the  truss  equal  to  one-eighth 
of  the  span. 

The  nearest  abutment,  or  point  of  support,  will  therefore 
support  seven-eighths  of  this  live  load  and  the  farthest  abut- 
ment will  support  one-eighth.  The  strains  on  the  chords  and 
braces  can  be  determined  by  the  methods  already  explained. 

The  strains  produced  upon  the  diagonals  between  the  end 
of  the  load  and  the  middle  of  the  truss,  by  the  one-eighth  of 
the  live  load  going  to  the  farthest  point  of  support  are  of  op- 
posite kind  to  those  which  would  be  produced  on  the  same 
pieces  by  the  dead  load.  That  is,  the  braces  whose  tops 
incline  towards  the  middle  of  the  truss  are  extended  by  the 
action  of  this  eighth  instead  of  being  compressed,  and  the 
other  braces  are  compressed  by  it  instead  of  being  extended. 
Some  of  the  braces,  therefore,  are  under  certain  circumstances, 
liable  at  one  time  to  be  extended  and  at  another  time  to  be 
compressed,  and  must,  in  consequence,  be  constructed  to  resist 
both  kinds  of  strains.  In  the  panel  system,  each  brace  is  gen- 
erally constructed  to  take  only  one  kind  of  strain.  Hence,  in 


DIMENSIONS   OF   TKTT8S.  347 

those  panels  where  a  change  of  strain  is  liable  to  take  place, 
another  brace  must  be  inserted  to  take  this  new  strain.  The 
braces  required  by  the  dead  load  are  called  main  braces : 
the  extra  braces  inserted  in  those  panels  where  a  change  or 
strain  may  occur,  are  called  counter -braces.  The  main 
braces  are  necessary  in  every  panel,  and  it  has  also  been  the 
custom  to  use  counter-braces  in  every  panel.  The  main  and 
counter-braces  generally  cross  each  other  in  the  middle  of  the 
panel,  the  angles  which  they  make  with  a  vertical  being 
supplements  of  each  other.  It  is  evident  that  there  is  no  ne- 
cessity for  counter-braces  in  any  of  the  panels  except  those 
between  the  extreme  positions  of  the  points  of  "  no  shear- 
ing "  strain  and  the  middle  of  the  truss. 

Length  and  Depth  of  a  Truss. 

462.  The  length  of  »a  truss  depends  upon  the  span  and 
whether  the  truss  is  to  rest  on  two  or  more  points  of  support. 
Assuming  that  the  truss  rests  on  two  points  of  support,  the 
length  depends  upon  the  span.  The  span  depends  upon 
several  things :  the  navigability  of  the  stream,  character  of 
the  freshets,  the  movement  of  ice,  the  practicability  of  obtain- 
ing inexpensive  and  good  foundations,  etc. 

Over  wide  river  bottoms,  marshes,  etc.,  where  good  founda- 
tions are  easily  procured  without  much  expense,  the  spans 
range  from  twenty-five  to  fifty  feet.  Over  important  rivers, 
from  150  to  250  feet. 

Extra  wide  spans  are  frequently  required  for  bridges  over 
the  main  channel  of  very  important  rivers.  The  central  span 
of  the  Victoria  Bridge,  over  the  St.  Lawrence  River,  is  330 
feet.  The  channel  spans  of  the  Louisville  bridge,  over  the 
Ohio  River,  are  370  and  400  feet  respectively.  The  central 
span  of  the  St.  Louis  bridge,  over  the  Mississippi  River,  is 
515  feet. 

The  depth  of  the  truss,  in  terms  of  its  length,  varies  from 
one-tenth  to  one-fifteenth  in  England  and  from  one-sixth  to 
one-tenth  in  the  United  States. 


The  Graphical  Method. 

463.  The  graphical  method  is  much  used  to  determine 
the  strains  on  the  different  parts  of  a  bridge  truss.  This 
method  possesses  many  advantages  and  grows  in  favor  with 
engineers  as  it  becomes  better  known. 


348 


CIVIL   ENGINEERING. 


By  its  use  the  engineer  is  enabled  to  make  an  independent 
investigation  of  the  strains  and  to  test  the  accuracy  of  his 
calculations  by  a  comparison  of  the  results  obtained  through 
two  independent  methods. 

The  graphical  method  is  based  on  the  simple  principles 
much  used  in  mechanics :  that  a  force  may  be  represented  by 
a  straight  line ;  that  the  force  is  completely  given  when 
the  length  of  the  line,  its  direction,  and  point  of  applica- 
tion are  known ;  and  that  if  two  forces  having  a  common 
point  of  application  are  given,  that  a  third  force  may  be 
determined,  which  acting  at  the  common  point  will  produce 
the  same  effect  as  the  two  acting  simultaneously.  This 
third  force  is  determined  by  the  use  of  the  principle  of  the 
"  parallelogram  of  forces." 

464.  Two  forces  having  a  common  point  of  applica- 
tion.— Suppose  two  forces,  P^  and  P2,  acting  at  the  point  At 
(Fig.  174). 

From  any  assumed  point,  as  0,  draw  a  right  line  parallel 
to  the  direction  of  the  force  Px,  and  lay  off  on  this  line,  ac- 


FIQ. 174 

cording  to  some  assumed  scale,  the  distance  0  M,  to  represent 
its  intensity.  From  the  end,  M,  of  the  distance  just  drawn,  draw 
the  line  M  N  parallel  and  equal  to  P2.  Join  N  and  0  by  a 
straight  line,  and  N  0  will  be  parallel  and  equal  to  the  result- 
ant of  P!  and  P2.  Its  intensity  can  be  obtained  by  measuring 
the  distance  0  N  with  the  same  scale  used  to  lay  off  0  M  and 
M  N. 

If  a  force  equal  to  and  parallel  to  N  0  acts  from  At  up- 
wards, there  would  be  an  equilibrium  among  the  three  forces 
at  AI.  It  therefore  follows  that  if  three  forces  at  any  point 
are  in  equilibrium,  the  three  sides  of  a  triangle,  which  are 
respectively  parallel  to  the  directions  of  these  forces,  may  be 
taken  to  represent  their  intensities. 


DETERMINING   THE   STBAIN.  349 

Assume  any  point,  as  C,  and  from  it  draw  to  the  extrem- 
ities 0  and  N  of  0  N,  the  right  lines  C  N  and  C  0.  These 
distances,  C  N  and  C  C,  may  be  taken  as  the  intensities  of  two 
components  which,  acting  at  Ax  in  directions  parallel  to  these 
lines  respectively  may  be  used  to  replace  the  resultant,  0  N. 

And  in  general,  any  two  right  lines  drawn  from  any  as- 
sumed point,  which  may  be  called  the  pole,  to  the  ends  of 
the  straight  line  representing  a  force,  may  represent  the  com- 
ponents of  that  force. 

465.  Any  number  of  forces  in  the  same  plane  having 
a  common  point  of  application. — Whatever  be  the  number 
of  forces  acting  at  A1?  the  right  lines  representing  them  in  in- 
tensity, if  drawn  parallel  to  their  directions  and  in  order, 
either  from  the  right  to  the  left  or  the  reverse,  each  from  the 
end  of  the  other,  will  form  a  polygon  whose  sides  may  be 
taken  to  represent  the  forces,  acting  at  Aj. 

If  the  last  line  drawn  terminates  at  the  starting  point  of 
the  polygon,  the  forces  are  in  equilibrium ;  if  not,  then  the 
right  line  drawn,  joining  the  extremity  of  the  last  side  with 
this  point,  will  represent  the  force,  which,  being  added  to 
those  acting  at  A1?  will  produce  an  equilibrium. 

It  is  evident  that  if  a  diagonal  be  drawn  in  this  polygon,  it 
may  be  taken  as  the  resultant  of  the  forces  on  either  side  of 
it  and  may  be  used  to  replace  those  forces. 

The  polygon  constructed  by  drawing  these  lines  parallel  to 
the  forces  is  called  the  c<  force  polygon,"  and  when  it  ter- 
minates at  the  point  of  beginning,  the  polygon  is  said  to  be 
"  closed." 

If  the  forces  act  in  the  same  straight  line,  the  polygon 
becomes  a  right  line. 

466.  A  system  of  forces  in  the  same  plane  with  dif- 
ferent points  of  application. — It  will  only  be  necessary,  in 
this  case,  to  produce  the  lines  of  direction  until  they  inter- 
sect.    It  is  then  the  case  just  considered.     It  may  be  that 
the  point  of  intersection  will  not  be  found  within  the  limits 
of  the  drawing.     Under  this  supposition,  a  point  of  the  re- 
sultant may  be  determined  as  follows : 

Let  P!  and  P2  be  any  tw.o  forces  which  do  not  intersect 
within  the  limits  of  the  drawing,  their  points  of  application 
being  ^  and  A2  respectively.  (Fig.  175.) 

Draw  0  M  and  M  N,  respectively,  equal  and  parallel  to  Pt 
and  P2.  The  line  0  N  will  give  the  direction  and  intensity 
of  their  resultant.  From  any  point,  as  C,  draw  the  right 
lines,  0  C  and  C  N.  These  are  the  components  which  may 
be  taken  to  replace  0  N.  Assume  any  point  on  Pl9  as  a 


350 


CIVIL   ENGINEERING. 


and  draw  through  it  the  lines,  ao  and  ab  parallel  to  C  0  and 
M  C,  respectively.  Where  ab  intersects  P2,  as  at  &,  draw  ba 
and  bo  parallel  to  C  M  and  N  C.  Produce  the  lines  ao  and 
be  until  they  intersect.  Their  point  of  intersection  will  be 
one  point  of  the  resultant,  which  can  now  be  constructed.  The 
same  method  holds  good  if  the  forces  are  parallel.  If  there 
were  more  than  two  forces  the  same  method  can  be  used. 


FIG.  175, 


If  perpendiculars  are  let  fall  from  the  point  of  intersec- 
tion, <?,  upon  the  directions  of  the  forces  rl  and  P2,  it  can 
be  easily  shown  that  they  are  to  each  other  inversely  as  the 
forces.  That  is,  if  the  perpendicular  let  fall  on  Pt  is  repre- 
sented by^/,  and  that  on  P2  by  p" ,  that  there  is  the  following 
proportion : 

y :/'::?,:?,. 

This  is  also  true  for  the  perpendiculars  let  fall  from  any 
other  point  of  the  resultant. 

467.  Parallel  forces. — The  principal  forces  acting  on  en- 
gineering structures  are  due  to  the  action  of  gravity,  and  in 
these  discussions  such  forces  are  taken  as  parallel  and  vertical. 

Let  Pl5  P2,  P3,  etc.,  be  a  system  of  parallel  forces  acting  at 
the  points  Al5  A2,  A3,  etc.,  in  the  same  plane.  (Fig.  176.) 

Lay  off  from  0,  on  a  straight  line  parallel  to  A1?  Pl5  the  dis- 
tance 0  1  equal  to  its  intensity,  and  from  1  to  2,  the  inten- 
sity of  P2,  and  then  from  2  to  3^  the  intensity  of  P3,  etc.  The 
straight  line  of  0  5  will  be  the  force'  polygon,  and  in  this 
case  equal  to  the  resultant,  as  all  the  forces  are  acting  in  the 
same  direction.  From  any  assumed  point,  c,  as  a  pole,  draw 
straight  lines  to  0, 1,  2,  3,  etc.,  or  extremities  of  the  forces 
just  laid  off  on  the  line  0  5.  The  perpendicular,  C  H,  is 
called  the  "  pole  distance."  Assume  a  point  on  the  the  right 
of  P,,  as  #,  and  through  it  draw  a  straight  line  parallel  to  0  C 


GRAPHICAL   METHOD. 


351 


From  the  point  J,  where  this  line  intersects  P1?  or  Pt  pro- 
duced, draw  a  line  parallel  to  C  1,  and  from  the  point  where 
this  intersects  P2  produced,  draw  one  parallel  to  C  2,  etc., 
until  lines  parallel  to  all  the  lines  drawn  from  C  have  been 
drawn. 

These  forces  P1}  P2,  etc.,  may  be  supposed  to  act  at  these 
points,  b,  c,  d,  etc.  If  the  points  a  and  g  are  fixed,  and  the 
others  are  all  connected  by  flexible  cords,  the  whole  arrange- 


FIG.  176. 

ment  would  form  a  funicular  machine  or  polygon.  The 
three  forces  acting  at  any  one  of  these  points  are  represented 
by  the  three  sides  of  a  triangle,  and  are  therefore  in  equilib- 
rium. The  broken  line,  a,  b,  c,  d,  e,f,  g,  thus  formed,  is  called 
the  "  equilibrium  polygon." 

If  ab  and  gf  be  produced  until  they  intersect,  their  inter- 
section will  be  one  point  of  the  resultant  of  the  system  of 
forces,  and  the  resultant  may  at  once  be  constructed. 

468.  Suppose  ag  to  be  the  axis  of  a  beam  resting  in  a  hori- 
zontal position  upon  two  points  of  support  at  a  and  g,  and 
acted  upon  by  a  system  of  forces  whose  resultants  correspond 
in  direction  with  those  of  the  forces  P1?  P2,  P3,  etc.  In  order 
that  an  equilibrium  should  exist,  there  must  be  vertical  reac- 
tions acting  upwards  at  these  points,  a  and  <?,  and  their  sum 
must  be  equal  to  the  resultant.  Represent  these  reactions  by 
R!  and  Rg.  If  the  resultant  passes  through  the  middle  point 
of  this  line,  ag,  that  is,  if  the  forces  are  distributed  symetri- 
cally  with  respect  to  the  middle  point,  the  reactions  will  be 
equal  to  each  other. 

Examining  the  equilibrium  polygon,  it  is  seen  that  the  result- 
ant of  P!  and  P2  must  pass  through  the  intersection  of  ab  and 
cd\  that  the  resultant  of  R!  and  P1?  through  the  intersec- 
tion of  ag  and  bo ;  of  P1?  P2,  and  Ps,  through  the  intersection 
of  ab  and  de\  and  so  on.  A  simple  inspection  of  the  force 


352 


CIVIL   ENGINEERING. 


polygon  will  give  the  direction  and  intensity  of  any  of  these 
resultants. 

469.  Bending  moment  of  any  section,  and  the  shear- 
ing strain. — Let  it  be  required  to  determine  the  bending  mo 
ment  and  the  shearing  strain  on  any  section  of  a  beam  rest- 
ing on  two  points  of  support  and  holding  up  four  unequal 
weights  at  unequal  distances  apart. 

Theorem. — The  moment  of  a  force,  around  any  centre 
is  equal  to  the  "pole-distance  "  multiplied  by  a  straight  line 
drawn  through  this  centre  parallel  to  the  force  and  limited 
by  the  components  of  the  force. 


: 

Ja 


P: 


FIG.  177. 


Let  the  force,  P  (Fig.  177),  be  resolved  into  any  two  com- 
ponents, aCt  and  #C2,  which  are  represented  by  the  right  lines 
C  0,  C  P,  drawn  from  the  pole  to  the  ends  of  the  force  in  the 
force  polygon.  The  moment  of  P  with  respect  to  any  point, 
as  bj  is  P  x  ab.  From  C2  draw  the  line  C2^>,  perpendicular  to 
P.  This  is  equal  to  the  "  pole  distance,''  which  represent  by  H. 
Through  b  draw  cd  parallel  to  P,  and  limited  by  Cj  and  C2 
produced.  From  similar  triangles,  the  following  proportion 
is  obtained : 

P  :  H : :  cd  :  ab,    or    P  x  ab  =  H  x  cd, 

which  was  to  be  proved. 

In  Fig.  178  the  bending  moment  at  0'  is  R!  x  A  0',  which, 
as  has  just  been  shown,  is  equal  to  H  xppl ;  at  0"  the  bending 
moment  is  E-,  x  AO"  —  "W^xA'O".  The  components  of  Wa 
are  ab  and  be.  Hence  the  moment  of  Wx  at  0"  is  H  xp\p,,y 
and  the  total  moment  is  II  xp'p\. 

And  as  this  is  true  for  any  section,  it  is  seen  that  the  bend- 
ing moments  are  proportional  to  the  ordinates  drawn  from 
the  closing  line  to  the  sides  of  the  equilibrium  polygon.  And 
at  any  section,  it  is  equal  to  the  product  of  H  and  the  ordin- 


GRAPHICAL   METHOD. 


353 


ate  of  the  equilibrium  polygon  corresponding  to  the  section 
under  consideration. 


1       t*' 


FIG.  178. 


The  ordinate  is  measured  by  the  scale  used  for  the  equilib- 
rium polygon,  and  the  pole  distance,  H,  by  the  scale  for  the 
force  polygon.  These  may  be  drawn  on  the  same  or  different 
scales,  whichever  is  the  most  convenient. 

Representation  of  the  shearing  strain. — The  shearing 
force  between  ~R^  and  Wly  is  1^.  At  TV*!,  the  shearing  force  is 
Hi- Wl ;  at  W2,  it  is  R!- Wj— W2,  etc.  Hence,  the  line,  K!,  1, 
2,  3,  etc.,  represents  graphically  the  shearing  forces  for  all 
parts  of  the  beam. 

An  examination  of  the  figure  shows  that  the  shearing  force 
is  greatest  where  the  bending  moment  is  the  least,  and  the 
reverse. 

470.  Couples. — It  has  been  assumed,  in  the  previous  dis- 
cussions and  examples,  that  the  forces  were  in  equilibrium, 
or  by  the  addition  of  a  single  force  an  equilibrium  could  be 
established. 


*     * 

a/ 


FIG.  179. 


If  two  forces  form  a  couple,  they  cannot  be  replaced  by  a 
single  force.    Let  Px  and  P2  be  a  couple  (Fig.  179),  and  012 
the  force  polygon. 
23 


354 


CIVIL   ENGINEERING. 


It  is  seen  that  this  force  polygon  closes,  that  is,  the  result 
ant  is  zero.  From  any  point  on  Pt  draw  ac  and  ab  parallel  to 
C  0  and  1  C.  At  J,  where  ab  intersects  P2  or  P2  produced, 
draw  lines  parallel  to  C  1  and  2  C.  The  lines  ac  and  M  are  par- 
allel. Therefore  the  equilibrium  polygon  will  not  close,  or  the 
lines  will  intersect  at  an  infinite  distance.  A  result  which 
was  to  be  expected.  (Art.  98,  Analytical  Mechanics.) 

The  figure  shows  that  the  components  of  the  forces  I\  and 
P2,  which  act  in  the  direction  of  the  line  ab,  are  equal  and 
directly  opposed  to  each  other,  and  that  the  other  two  are 
parallel,  forming  a  couple.  Hence,  it  is  concluded  that  a 
couple  can  be  replaced  by  another  without  changing  the  ac- 
tion of  the  forces. 

From  what  has  been  shown,  it  is  evident  that  if  both  the 
force  and  equilibrium  polygon  close,  that  an  equilibrium  exists 
among  the  forces.  But  if  the  force  polygon  closes  and  the 
equilibrium  does  not,  that  the  forces  cannot  be  replaced  by  a 
single  force,  but  only  by  a  couple. 

471.  Influence  of  a  couple.— Let  A  B  (Fig.  180)  be  abeam 
fastened  at  its  ends  and  acted  upon  by  the  couple  P1  P2. 


FIG.  180. 


The  beam  being  fastened,  the  reactions  at  A  and  B  will 
keep  the  couple  from  moving  and  the  four  forces  will  be 
in  equilibrium.  Construct  the  force  polygon,  012,  and 
from  a  pole,  C,  draw  the  lines  C  0,  C  1.  Form  the  equilib- 
rium polygon,  a  1)  c  d,  of  the  forces  Pt  P2 ;  produce  ~b  a  and 
c  d  until  they  intersect  the  lines  of  direction  of  the  reac- 
tions ;  join  a  and  d  and  this  will  be  the  closing  line  of  the 
polygon.  Parallel  to  this  line  draw  Cg  in  the  force  polygon. 
An  examination  of  the  force  polygon  shows  that  0  g  is  the 
vertical  reaction  acting  downwards  at  B,  and  g  0,  the  reaction 
at  A,  acting  upwards,  which  with  the  couple  Pj  P2  form  an 
equilibrium. 

The  ordinates  drawn  from  the  closing  line,  ad,  upon  the 
sides,  ab,  bo,  and  ad,  multiplied  by  the  pole  distance  give 
the  bending  moments  for  the  corresponding  sections  of  the 
beam. 


GRAPHICAL  METHOD. 


355 


In  the  preceding  examples  the  force  polygon  has  been  given, 
and  from  it  the  equilibrium  polygon  has  been  constructed. 
Inversely,  the  equilibrium  polygon  being  given,  the  force 
polygon  is  easily  constructed. 

472.  From  the  preceding  demonstrations,  the  following 
theorem  may  be  enunciated  : 

Theorem. — If  straight  lines  be  drawn  through  any  as- 
sumed point  parallel  to  the  sides  of  a  polygonal  frame,  then 
the  sides  of  any  polygon  whose  angles  lie  on  these  radiating 
lines  may  be  taken  to  represent  a  system  of  forces  which,  if 
applied  to  the  angular  points  of  theframe^  will  be  in  equi- 
librium among  themselves.  And  the  converse,  that  if  a  sys- 
tem of  external  forces  acting  at  the  angles  of  a  frame  are  in 
equilibrium^  that  from  an  assumed  point  drawing  straight 
lines  parallel  to  the  sides  of  the  frame,  and  then  parallel  to 
the  directions  of  these  forces  drawing  straight  lines  whose 
successive  intersections  are  on  the  successive  radial  lines,  the 
distances  cut  off  by  the  second  set  will  represent  the  strains 
on  the  corresponding  sides  of  the  frame. 

Let  ABC  (Fig.  181)  be  a  triangular  frame  acted  upon  at 
the  points  A  B  C  by  a  system  of  external  forces  which  are  in 
equilibrium.  Let  Pj  P2  P8  be  the  resultants  of  the  forces  act- 
ing at  these  points,  and  suppose  that  these  resultants  are  in 
the  plane  ABC. 

From  an  assumed  point,  P,  draw  the  straight  lines,  P 1,  P  2, 


FIG.  181. 
• 

and  P  3,  respectively,  parallel  to  the  sides  A  B,  B  C,  and  C  A. 
Through  an  assumed  point,  as  0,  on  the  line  P  3,  draw  the  line 
0  M  parallel  to  the  direction  of  the  force  P1?  and  from  its  point 
of  intersection  with  P 1,  draw  the  line  M  N  parallel  to  the 
force  P2. 

Join  N  and  0  by  a  straight  line,  and  this  will  be  parallel  to 
the  force  P8.     The  triangle,  0  M  N,  will  be  the  force  polygon. 

The  distance,  P  0,  will  measure  the  force  acting  along  the 
piece  AC;  P  M,  that  along  A  B;  and  P  N,  that  along  B  C. 


356  CIVIL   ENGINEERING. 

If  the  external  forces  are  parallel  the  polygon  becomes  a 
straight  line,  which  will  be  divided  into  segments  by  the  lines 
drawn  parallel  to  the  sides  of  the  frame.  Each  segment  will 
represent  the  external  force  acting  at  one  of  the  angles  of 
the  frame,  and  the  distances  cut  oft  will  represent  the  forces 
acting  along  the  adjacent  pieces. 

An  application  of  these  principles  will  enable  the  student 
to  determine  graphically  the  strains  on  the  different  parts  of 
a  frame,  and  test  the  accuracy  of  calculations  already  made 
by  other  methods. 

Working,  Proof,  and  Breaking  Loads. 

473.  Ultimate  strength  of  a  structure. — The  object  of 
the  calculations  made  to  determine  the  strength  of  a  given 
structure  is  to  find  the  load  which,  placed  on  the  structure, 
will  cause  it  to  give  way  or  break  in  some  particular  way. 
This  load  is  called  the  ultimate  strength  or  breaking  load 
of  the  structure. 

Working  load. — As  the  bridge  must  not  be  liable  to  yield 
or  give  way  under  any  load  which  it  is  expected  to  carry, 
it  is  made  several  times  stronger  than  is  actually  necessary  to 
sustain  the  greatest  load  which  it  will  ever  have  to  support. 
The  greatest  load  thus  assumed  is  called  the  working  load. 

The  ratio  of  the  breaking  load  to  the  working  load,  or 
"  factor  of  safety,"  is  assumed  arbitrarily,  limited  by  experi- 
ence. It  is  usually  taken  from  four  to  six  for  iron,  and  even 
as  high  as  ten  for  wooden  bridges.  It  should  be  large  enough 
to  ensure  safety  against  all  contingencies,  as  swift  rolling 
loads,  imperfect  materials,  and  poor  workmanship. 

Proof  load. — When  the  bridge  is  completed,  it  is  usual  to 
test  the  structure  by  placing  on  it  a  load  greater  than  it  will 
ever  have  to  support  in  practice.  A  train  of  locomotives  for 
a  railroad  bridge,  and  a  crowd  of  men,  closely  packed,  upon 
an  ordinary  road  bridge,  are  examples.  These  loads  are 
known  as  proof  loads. 

A  proof  load  should  remain  on  the  bridge  but  for  a  short 
time,  and  should  be  removed  carefully,  avoiding  all  shocks. 
Excessive  proof  loads  do  harm  by  injuring  the  resisting  pro- 
perties of  the  materials  of  which  the  bridge  is  built. 

Wooden  Bridge-trusses. 
474-,  Both  the  king  and  queen-post  trusses,  as  stated  in  a 


LATTICE   TRUSS. 


357 


previous  article,  are  frequently  made  entirely  of  wood,  and 
are  used  in  bridges  of  short  spans. 

A  compound  truss,  entirely  of  wood,  the  outline  of  which 
is  shown  in  Fig.  182,  has  been  used  in  bridges  for  spans  oi 
considerable  width. 


FIG.  182. 


The  celebrated  bridge  at  Schaffhausen,  which  consisted  of 
two  spans,  the  widest  being  193  feet,  was  built  upon  this 
principle. 

475.  Town's  lattice  truss. — This  truss  was  made  entirely 
of  wood,  and  at  one  time  was  much  used  in  bridge  construc- 
tion. It  belongs  to  the  triangular  system.  The  chords  (Fig. 
183)  were  built  of  beams  of  timber,  and  frequently  of  plank  of 
the  same  dimensions  as  that  used  for  the  lattice.  They  were 
in  pairs,  embracing  the  diagonals  connecting  the  upper  and 
lower  chords.  The  diagonals  were  of  plank,  of  a  uniform 
thickness  and  width,  equally  inclined  towards  the  vertical  and 
placed  at  equal  distances  apart.  They  were  fastened  to  the 
chords,  and  to  each  other  at  their  intersections,  by  treenails, 
as  shown  in  the  figure. 


I  I 


FIG.  183. 


This  truss  was  frequently  made  double.     In  case  the  lat- 
tices were  separated  by  a  middle  beam,  as  shown  in  the  cross- 


358 


CIVIL   ENGENEEEING. 


section  in  Fig.  183,  the  chords,  instead  of  being  in  pail's, 
were  made  of  three  beams,  placed  side  by  side. 

When  the  truss  was  of  considerable  depth,  intermediate 
longitudinal  beams  were  used  to  stiffen  the  combination,  as 
shown  in  the  figure. 

This  truss  possessed  the  advantages  of  a  simple  arrange- 
ment of  its  parts  and  ease  of  construction.  It  also  possessed 
the  disadvantages  of  a  waste  of  material  and  a  faulty  con- 
struction by  which  the  strength  of  the  truss  depended  upon 
the  strength  and  the  perfect  fitting  of  the  treenails. 


n 


U 


U 


FIG.  184 — Represents  a  panel  of  Long's  truss. 
A  and  B,  upper  and  lower  chords. 

C,  C,  uprights,  in  pairs. 

D,  main  braces,  in  pairs. 

E,  counter-brace,  single. 

a,  a,  mortises  where  gibs  and  keys  are  inserted. 
&,  &,  blocks  behind  uprights,  fastened  to  the  chord. 

F,  gib  and  key  of  hard  wood. 

476.  Long's  truss. — This  truss  belongs  to  the  panel  sys 
tern,  and  was  built  entirely  of  wood.  It  was  one  of  the  earlier 
trusses  used  in  the  United  States,  and  takes  its  name  from 


LONG'S  AND  BURR'S  TRUSSES. 


359 


Colonel  Long,  of  the  Corps  of  Engineers,  United  States 
Army,  who  invented  it.  It  was  one  of  the  first  trusses  in 
which  a  scientific  arrangement  of  the  parts  was  observed. 

" 


.11  the  timber  used  in  its  construction  had  the  same  dimen- 
sions in  cross-section. 

Each  chord  was  composed  of  three  solid-built  beams,  placed 
side  by  side,  with  sufficient  intervals  between  them  to  allow  of 
the  insertion  of  the  uprights.  The  uprights  which  connected 
the  chords  were  in  pairs,  and  fastened  to  the  chords  by  gibs 
and  keys.  These  gibs  were  inserted  in  rectangular  holes  made 
in  the  chords,  and  fitted  in  shallow  notches  cut  in  the  up- 
rights. Pieces  of  wood  wide  enough  to  fill  the  space  between 
the  beams,  about  three  or  four  inches  thick  and  two  feet  long, 
were  inserted  between  the  beams  of  the  chords,  behind  the 
uprights,  and  fastened  to  the  beams  by  treenails.  These  were 
for  the  purpose  of  strengthening  the  uprights  and  preventing 
their  yielding  at  the  notches. 

The  main  braces  were  in  pairs,  and  were  joined  to  the  up- 
rights, as  shown  in  the  figure.  The  counter-braces  were  single, 
and  were  placed  between  the  main  braces,  abutting  against 
or  fastened  upon  the  upper  surface  of  the  middle  beam  of 
the  chords.  Generally  they  were  fastened  to  the  main  braces 
by  treenails  at  their  intersections. 


Fia.  185. 


477.  Burr's  truss. — This  is  another  of  the  earlier  wooden 
trusses,  much  used  at  one  time  in  the  United  States.  This 
truss  (Fig.  185)  belongs  to  a  compound  system,  being  com- 
posed of  a  truss  of  the  panel  system,  stiffened  by  solid-built 


360 


CIVIL   ENGINEERING. 


curved  beams,  called  arch  timb'ers.  These  arch  timbers 
were  in  pairs,  embracing  the  truss  and  fastened  to  it  at  the 
different  intersections  of  the  pieces  of  the  truss  with  the 
curved  beams,  as  shown  in  the  figure. 

478.  Other  forms  of  wooden  trusses. — The  trusses  al- 
ready named  may  be  considered  as  typical  trusses.  There 
are  many  others,  all  of  which  may  be  referred  to  one  of  the 
systems  already  given,  or  a  combination  of  those  systems. 
Haupt's  lattice,  Hall's  lattice,  McCallum's  truss,  etc.,  are 
examples  of  some  of  the  different  forms  of  wooden  bridge- 
trusses. 


Bridge-trusses  of  Wood  and  Iron. 

479.  Canal  bridge. — A  truss  composed  of  wood  and  iron, 
which  has  been  much  used  for  common  road  bridges  over  the 
New  York  State  canals,  is  shown  in  Fig.  186. 


FIG.  186. 

In  this  truss,  the  chords  and  diagonals  are  of  wood,  and 
the  verticals  of  iron.  In  some  cases,  the  lower  chord  is  also 
of  iron. 

480.  Howe's  truss. — A  popular  truss  for  bridges,  both 
common  and  railroad,  and  one  which  has  probably  been 
used  more  than  any  other,  is  known  as  the  Howe  truss. 
(Fig.  187.) 

This  truss  belongs  to  the  panel  system.  The  chords  and 
braces  are  made  of  wood,  and  the  verticals  of  iron. 

The  chords  are  solid-built  beams  of  uniform  cross-section 
throughout. 

The  braces  are  also  of  uniform  size,  the  main  braces  being 
in  pairs,  and  the  counter-braces  single,  &nd  placed  between 
the  main  braces,  as  in  Long's  truss.  Between  the  ends  of 


HOWE'S  AND  JPBATT'S  TRUSSES. 


361 


the  braces  and  the  chords,  blocks  of  hard  wood  or  of  cast  iron, 
inserted  in  shallow  notches  in  the  chords,  are  used  as  shown 
in  the  figure.  The  faces  of  the  blocks  should  be  at  right 
angles  to  the  axes  of  the  braces. 


FIG.  187. 


The  verticals  are  in  pairs,  and  pass  through  the  blocks  and 
chords,  and  are  secured  by  nuts  and  screws  at  both  ends,  or 
by  heads  at  the  ends  witn  a  nut  and  screw  arrangement  at 
the  middle.  By  tightening  the  screws,  the  chords  are  drawn 
towards  each  other,  and  the  reverse.  To  prevent  the  edges 
of  the  nuts  from  pressing  in  and  injuring  the  timber,  washers, 
or  iron  plates,  are  placed  between  the  nut  and  the  wood. 

Where  the  pressure  on  the  block  is  great,  an  iron  block  or 
other  arrangement  is  placed  between  the  block  on  one  side 
and  the  washer  on  the  other,  to  prevent  the  block  from 
crushing  into  the  chord. 

It  is  seen  that  there  is  an  excess  of  material  in  some  of  the 
chords  and  the  braces.  The  corresponding  gain  obtained  in 
reducing  the  amount  of  material,  by  proportioning  the  pieces 
to  the  strains  they  would  have  to  support,  would  not  pay  the 
cost  of  extra  time  and  labor  required  ;  these  pieces  are  there 
fore  made,  as  a  rule,  with  a  uniform  cross-section. 

There  would  be  a  gain  if  the  verticals  were  proportioned  to 
the  strains  which  they  have  to  support,  instead  of  being  made 
of  uniform  size. 

It  is  observed  that  the  framing  is  such  that  the  diagonals 
will  only  take  a  compressive  strain,  and  the  verticals  a  tensile 
one. 

481.  Pratt;s  truss. — If  the  framing  of  the  Howe  truaa 
is  changed  so  that  the  diagonals  will  only  take  a  tensile  strain, 
and  the  verticals  a  compressive  one,  there  results  the  trusi 


CIVIL   ENGINEERING. 

known  as  Pratt's.     The  chords  and  verticals  in  this  case  are 
of  wood,  and  the  diagonals  are  of  iron. 

482.  There  are  quite  a  number  of  trusses  besides  those 
just  named,  which  are  composed  of  wood  and  iron.  Those 
mentioned  are  typical  ones,  and  illustrate  fully  the  method 
}f  combining  the  two  materials  in  the  same  structure. 


Iron  Bridge-trusses. 

483.  Bridge-trusses  made  entirely  of  iron,  or  of  iron  and 
steel  are  much  used  at  the  present  time. 

Trusses  of  iron  belong  to  the  three  systems  already 
described,  viz :  the  triangular,  the  panel,  and  the  bow- 
string systems,  and  are  generally  known  by  the  names  of 
their  inventors. 

At  one  time,  the  use  of  cast-iron  for  the  compressive 
members  of  a  truss  was  much  favored  by  builders  in  the 
United  States.  At  the  present  time,  wrought  iron  or  steel 
is  preferred  to  cast-iron  for  all  the  parts  of  a  truss. 

The  trusses  known  as  Fink's,  Bollman's,  Warren's.  Jones, 
WhippleX  Murphy- Whipple,  Linville,  Post's,  etc.,  are  some 
of  the  trusses  made  entirely  of  iron  which  are  most  frequently 
seen  in  use  in  the  United  States. 

Fink's  truss. — The  principles  of  Fink's  truss  are  given  in 
Art.  449.  The  arrangement  of  its  parts  enables  the  truss  to 
resist  in  the  best  manner  the  effect  produced  by  a  moving 
load,  or  by  changes  of  temperature.  The  lower  extremities 
of  the  verticals  being  free  to  move,  the  verticals  remain 
normal  to  the  curve  assumed  by  the  chord  under  the  strain- 
ing force,  and  the  distances  of  their  lower  ends  from  the  con- 
nection of  the  ties  with  the  chord  remain  relatively  the 
same.  None  of  its  parts  are  therefore  unequally  strained  by 
the  force  producing  the  deflection. 

Bollman's  truss. — The  principle  on  which  this  truss  is 
constructed  is  mentioned  in  Art.  450.  In  order  to  avoid  the 
ill  effects  of  unequal  expansion  or  contraction  of  the  ties  pro- 
duced by  changes  of  temperature,  a  compensating  link  is 
used,  by  means  of  which  the  pin  holding  the  ties  is  enabled 
to  change  its  position  as  the  ties  contract  or  expand,  without 
straining  the  verticals. 

Warren's  truss. — The  principle  of  this  truss  is  explained 
in  Article  451.  It  is  ordinarily  made  entirely  of  wrought 
iron.  In  some  cases  the  braces  are  of  cast  iron,  in  the  form 
of  hollow  pillars,  with  wrought-iron  ties  enclosed.  The  brace 


WHIPPLE'S  AND  POST'S  TBTTSSES. 


363 


is  thus  composed  of  two  distinct  parts,  and  is  better  suited  to 
resist  the  strains  which  it  has  to  sustain. 

Jones's  truss. — This  truss  is  the  Howe  truss  in  principle, 
all  the  parts  being  of  iron. 

Whipple's  truss. — This  truss  is  one  of  the  first  used 
in  this  country  made  entirely  of  iron.  It  is  composed  of 
cast  and  wrought  iron ;  the  former  being  used  for  the 
compression  members,  and  the  latter  for  the  tension  mem- 
bers. 

This  truss  (Fig.  188)  belongs  to  the  panel  system.  The 
upper  chord  is  usually  made  of  hollow  tubes  of  cast  iron,  in 
sections,  whose  lengths  are  each  equal  to  a  panel  distance. 


FIG.  18& 


The  lower  chord  is  made  of  links,  or  eye-bars,  of  wrought 
iron,  which  fit  upon  cast-iron  blocks.  These  blocks  hold  the 
lower  ends  of  the  vertical  pieces. 

The  vertical  pieces  are  of  cast  iron,  and  are  so  made  that 
the  inclined  pieces  can  pass  through  the  middle  of  them. 
The  parts  are  frequently  trussed  by  iron  rods,  to  prevent 
bending. 

The  inclined  pieces  are  wrought-iron  rods,  and  it  is  seen 
that  each  of  them,  excepting  those  at  the  ends,  crosses  two 
panels. 

An  examination  of  this  truss  shows  that  the  inventor  has 
considered  economy  of  material  in  making  the  verticals, 
struts,  and  the  diagonals,  ties.  In  principle  it  corresponds 
with  the  Pratt  truss. 

Murphy- Whipple  truss. — This  is  the  Pratt  truss,  entirely 
of  iron,  with  some  of  the  details  of  Whipple's. 

JLinville  truss. — This  is  Whipple's  truss  made  entirely 
of  wrought  iron,  the  verticals  being  wrought-iron  tubular 
columns. 

Post's  truss. — This  truss  is  composed  of  cast  and  wrought 
iron.  Its  peculiarity  lies  principally  in  its  form  (Fig.  189) ; 


364:  CIVIL   ENGINEERING. 

the  struts,  instead  of  being  vertical,  are  inclined  towards  the 
centre  of  the  bridge,  making  an  angle  of  about  23°  30'  with 
the  vertical,  as  shown  in  the  figure.  The  ties  cross  two  panels, 
and  make  an  angle  of  45°  with  the  vertical.  The  counter- 
ties  make  the  same  angle,  but  cross  only  one  panel. 


FIG.  189. 


The  inclination  given  to  the  struts  was  for  the  purpose  of 
obtaining  the  same  strength  with  a  less  amount  of  material 
than  that  obtained  when  the  struts  were  vertical. 

Lattice  trusses.  —  Lattice  trusses,  made  entirely  of  iron, 
are  frequently  used  in  railroad  bridges.  They  do  not  differ 
in  principle  from  the  lattice  truss  made  of  wood. 


Continuity  of  the  Truss. 

Various  opinions  have  been  held  as  to  the  advantages 
obtained  in  connecting  the  trusses  over  adjacent  spans,  so 
that  the  whole  arrangement  should  act  as  a  single  beam. 

If  the  load  is  permanent,  or  the  weight  of  the  structure 
is  very  great,  compared  with  the  moving  load,  it  is  advisable 
to  connect  the  trusses,  so  that  they  shall  act  as  a  single  con- 
tinuous beam. 

But  when  this  is  not  the  case,  the  effect  of  a  heavy  load  is 
to  reverse  the  strains  on  certain  members  of  the  trusses  over 
the  adjacent  spans ;  a  result  which  is  to  be  avoided,  and  hence 
the  trusses  are  ordinarily  not  rigidly  connected. 


WROUGHT-IEON   BRIDGES.  365 


CHAPTER  XV 

IL-  -TUBULAR   AND   IRON    PLATE    BRIDGES. 

485.  Bridges  of  this  class  are  made  entirely  of  wrought 
iron. 

A  tubular  girder  is  one  which  is  made  of  iron  plates, 
so  riveted  together  as  to  form  a  hollow  beam.  These  girders 
may  be  placed  side  by  side  and  a  roadway  built  upon  them, 
forming  a  simple  bridge,  which  in  principle,  would  not  differ 
from  the  simple  bridge  described  in  Art.  435. 

When  the  tube  is  made  large  enough  to  allow  the  roadway 
to  pass  through  it,  it  is  called  a  tubular  bridge. 

The  difference  in  construction  between  the  tubular  bridges 
and  the  tubular  girders  consists  in  the  arrangements  made  to 
stiffen  the  four  sides  of  the  tube. 

The  three  great  examples  of  tubillar  bridges  are  the  Bri- 
tannia Bridge,  across  the  Menai  Straits,  in  Wales ;  the  Conway 
Bridge,  over  the  Conway  River,  in  Wales ;  and  the  Victoria 
Bridge,  over  the  St.  Lawrence  River,  at  Montreal,  Canada. 

The  Britannia  Bridge  consists  of  two  continuous  girders, 
each  1,487  feet  long,  resting  on  three  piers  and  two  abut- 
ments. Each  tube  is  fixed  to  the  central  pier  and  is  free  to 
move  on  rollers  placed  on  the  other  piers  and  abutments. 
The  middle  spans  are  459  feet  each,  and  the  shore  spans  are 
230  feet  each.  The  bridge  is  100  feet  above  the  surface  of 
the  water. 

The  Conway  Bridge  consists  of  two  tubes,  separated  by  a 
few  feet,  over  a  span  of  400  feet. 

The  Victoria  Bridge  is  a  single  tube,  6,538  feet  long,  rest- 
ing on  piers,  forming  twenty-four  spans  of  242  feet  each,  and 
a  centre  span  of  330  feet,  or  twenty-five  spans  in  all.  The 
tube  is  made  continuous  over  each  set  of  two  openings,  the 
middle  of  the  tube  being  fixed  at  the  centre  pier  of  the  open- 
ing and  the  extremities  being  free  to  move  on  rollers  placed 
on  the  adjacent  piers. 

The  centre  span  is  level,  and  is  about  sixty  feet  above  the 
surface  of  the  water.  From  the  centre  span  the  bridge  slopes 
downward  at  an  inclination  of 


366 


CIVIL   ENGINEERING. 


In  the  Con  way  and  Britannia  bridges,  the  tops  and  bottoms 
are  made  cellular ;  that  is,  the  plates  are  so  arranged  as  to 
form  rows  of  rectangular  cells  (Fig.  190).  The  joints  of  the 
cells  are  connected  and  stiffened  by  covering  plates  on  the 
outside  and  by  angle-irons  within. 


till 


FIG.  190. 


FIG.  191. 


The  top,  A,  is  composed  of  eight  cells,  each  of  which  is  one 
foot  and  nine  inches  wide,  and  one  foot  and  nine  inches  high, 
interior  dimensions  The  bottom,  C,  is  divided  into  six  cells, 
each  of  which  is  two  feet  and  four  inches  in  width,  and  one 
foot  and  nine  inches  high.  These  dimensions  are  sufficiently 
large  to  admit  a  man  for  painting  the  interior  of  the  cells  and 
for  repairs. 

The  sides,  B,  are  composed  of  plates  set  up  on  end  (Fig. 
192),  their  edges  adjoining,  and  connected  by  means  of  verti- 
cal T-iron  ribs,  /*,  f  (Fig.  190).  The  horizontal  joints  of  the 
side  plates  are  fastened  by  covering  strips.  The  connection 
between  the  sides  and  top  and  bottom  is  strengthened  by 
gussets,  A,  A,  riveted  to  the  interior  T-irons. 


WROTTGHT-IROX   BRIDGES. 


367 


FIG.  192. 


In  the  Victoria  Bridge  the  top  and  bottom,  instead  of  being 
cellular,  consist  of  layers  of  plates  riveted  together  and  stif- 
fened by  means  of  ribs  (Fig.  191).  The 
top.  A,  is  slightly  arched,  and  is  stiffened 
by  longitudinal  T-irons,  d,  d,  d,  placed 
about  two  feet  three  inches  apart,  and  by 
transverse  ribs,  0,  about  seven  feet  apart. 
The  bottom,  c,  is  stiffened  by  T-shaped 
beams,  g,  which  form  the  cross-pieces  of 
the  roadway. 

Erection, — There  are  three  methods 
which  have  been  used  to  place  tubular 
bridges  in  position  :  1,  building  the  tube 
on  the  ground,  and  then  lifting  it  into 
place ;  2,  constructing  the  tube,  and 
moving  it  endwise  upon  rollers,  on  the 
piers ;  and  3,  building  it  in  position  on  a  scaffold. 

The  first  of  these  methods  was  adopted  for  the  Britannia 
Bridge  and  the  third  for  the  Victoria  Bridge. 

Cambering. — If  the  top  and  bottom  of  the  tube  were  made 
horizontal,  the  tube  would  when  placed  in  position  suffer 
deflection  at  the  middle  point  from  its  own  weight.  In  order 
that  it  may  be  horizontal  after  it  has  fully  settled  in  position, 
the  tube  is  made  convex  upwards.  This  convexity  is  called 
the  camber  of  the  tube  or  truss.  The  expression  for  maxi- 
mum deflection  of  a  beam  in  a  horizontal  position  resting 
upon  two  points  of  support  will  give  the  amount  of  camber  to 
give  the  tube.  The  camber  given  the  Britannia  Bridge  was 
eighteen  inches. 

^Remark. — Tubular  bridges  of  these  types  are  not  now  in 
much  favor  with  the  engineering  profession,  and  few,  if  any, 
will  ever  be  built  in  the  future.  The  same  amount  of  mate- 
rial in  the  form  of  a  truss  bridge  will  give  a 
better  bridge. 

486.  Plate  bridges. — If  we  were  to  sup- 
pose the  top  removed  from  the  tubular  bridge, 
or  to  suppose  the  diagonals  of  the  lattice  truss 
to  be  multiplied  until  the  side  was  a  con- 
tinuous piece,  we  would  obtain  the  plate 
girder.  In  cross-section,  the  girder  is  x-form 
(Fig.  193).  Its  general  construction  conforms 
to  that  given  for  the  tubular  bridge. 

The  joints  of  the  flanges,  A  and  B,  are  con-     1~<!I     Tjjl  'B 
nected  by  covering  plates;  the  web,  C,  is  gen- 
erally of  thin  plate.     The  web  and  flanges  are  fastened  by 


368  CIVIL  ENGINEERING. 

angle-irons,  D,  riveted  to  both  of  them.     The  sides  are  stif- 
fened by  T-irons,  as  in  the  tubular  bridges. 

The  advantages  gained  by  using  this  class  of  bridges  are 
confined  to  shallow  bridges  of  moderate  span.  When  the 
span  exceeds  sixty  feet,  it  is  more  economical  to  use  one 
of  the  iron  trusses  already  named. 


CHAPTEE    XYL 

in.— ARCHED    BRIDGES. 

487.  Arched  bridges  are  made  either  of  masonry,  of  iron, 
or  of  steel. 

The  form  of  arch  most  generally  used  is  the  cylindrical. 
The  form  of  soffit  will  be  governed  by  the  width  of  the 
span,  the  highest  water  level  during  the  freshets,  the  ap- 
proaches to  the  bridge,  and  the  architectural  effect  which 
may  be  produced  by  the  structure,  as  it  is  more  or  less  ex- 
posed to  view  at  the  intermediate  stages  between  high  and 
low  water. 

Oval  and  segment  arches  are  mostly  preferred  to  the  full 
centre  arch,  particularly  for  medium  and  wide  bays,  for  the 
reasons  that  for  the  same  level  of  roadway  they  afford  a 
more  ample  water-way  under  them,  and  their  heads  and 
spandrels  offer  a  smaller  surface  to  the  pressure  of  the  water 
during  freshets  than  the  full  centre  arch  under  like  circum- 
stances. 

The  full  centre  arch,  from  the  simplicity  of  its  construc- 
tion and  its  strength,  is  to  be  preferred  to  any  other  arch  for 
bridges  over  water-courses  of  a  uniformly  moderate  current, 
and  which  are  not  subjected  to  considerable  changes  in  their 
water-levels,  particularly  when  its  adoption  does  not  demand 
expensive  embankments  for  the  approaches. 

If  the  spans  are  to  be  of  the  same  width,  the  curves  of  the 
arches  should  be  the  same  throughout.  If  the  spans  are  to 
be  of  unequal  width,  the  widest  should  occupy  the  centre  of 
the  structure,  and  those  on  each  side  of  the  centre  should 
either  be  of  equal  width,  or  else  decrease  uniformly  from  the 
centre  to  each  extremity  of  the  bridge.  In  this  case  the 
curves  of  the  arches  should  be  similar,  and  the  springing 
lines  should  be  on  the  same  level  throughout  the  bridge. 


ABCHED  BRIDGES.  369 

The  level  of  the  springing  lines  will  depend  upon  the  rise 
of  the  arches,  and  the  height  of  their  crowns  above  the  water- 
level  of  the  highest  freshets.  The  crown  of  the  arches  should 
not,  as  a  general  rule,  be  less  than  three  feet  above  the  high- 
est known  water-level,  in  order  that  a  passage-way  may  be 
left  for  floating  bodies  descending  during  freshets.  Between 
this,  the  lowest  position  of  the  crown,  and  any  other,  the  rise 
should  be  so  chosen  that  the  approaches,  on  the  one  hand, 
may  not  be  unnecessarily  raised,  nor,  on  the  othe  other,  the 
springing  lines  be  placed  so  low  as  to  mar  the  architectural 
effect  of  the  structure  during  the  ordinary  stages  of  the  water. 

488.  Masonry  arches. — These  may  be  of  stone,  of  brick, 
or  of  mixed  masonry.  The  methods  of  construction,  already 
described  under  the  heads  of  Foundations  and  Masonry,  are 
applicable  to  the  construction  of  masonry  arches  used  for 
bridges.  As  the  foundations  and  beds  of  the  piers  and  abut- 
ments are  exposed  to  the  action  of  the  water,  precaution 
should  be  taken  to  secure  them.  (Art.  440.) 

Centres. — The  centres  used  should  be  strong,  so  as  to  settle 
as  little  as  possible  during  the  construction  of  the  arch,  and 
for  wide  spans,  should  be  so  constructed  that  they  can  be 
removed  without  causing  extra  strains  on  the  arch.  This  is 
effected  by  removing  the  centering  from  the  entire  arch  at 
the  same  time.  Removing  the  centering  is  termed  striking 
the  centre. 

In  wide  spans,  the  centres  are  struck  by  means  of  an 
arrangement  of  wedge  blocks,  termed  striking  plates.  This 
arrangement  consists  in  forming  steps  upon  the  upper  surface 
of  the  beam  which  forms  the  framed  support  for  the  centre. 
On  this  a  wedge-shaped  block  is  placed,  on  which  rests  an- 
other beam,  having  its  under  surface  also  arranged  with  steps. 
The  struts  of  the  rib  of  the  centering  either  abut  against  the 
upper  surface  of  the  top  beam,  or  else  are  inserted  into  cast- 
iron  sockets,  termed  shoe-plates,  fastened  to  this  surface. 
The  centre  is  struck  by  driving  back  the  wedge  block.  When 
the  struts  rest  upon  intermediate  supports  between  the  abut- 
ments, folding  wedges  may  be  placed  under  the  struts,  or  else 
upon  the  back  pieces  of  the  ribs  under  each  bolster.  The 
latter  arrangement  presents  the  advantage  of  allowing  any 
part  of  the  centre  to  be  eased  from  the  soffit,  instead  of  de- 
taching the  whole  at  once,  as  in  the  other  methods  of  striking 
wedges. 

Another  method  of  striking  centres  is  by  the  use  of  sand. 
In  this  method,  the  centres  rest  upon  cylinders  filled  with  sand. 
These  cylinders  are  arranged  so  that  the  sand  can  run  out 
24 


370 


CIVIL   ENGINEERING. 


slowly  near  the  bottom.  When  ready  to  strike  the  centre, 
the  sand  is  allowed  to  run  out  of  the  cylinders,  and  all  the  ribs 
gradually  and  evenly  settle  down  away  from  the  soffit.  The 
sand  having  run  out,  the  centre  can  then  be  removed  in  the 
ordinary  manner. 

489.  Iron  arched  bridges. — Next  to  masonry,  cast  iron  is 
the  material  best  suited  for  an  arched  bridge.     It  combines 
great  resistance  to  compression  or  strength,  with  durability 
and  economy ;  qualifications  already  given  as  requisite  for  an 
engineering  structure. 

Wrought  iron  is  sometimes  used  for  arched  bridges.  Where 
the  bridge  is  liable  to  considerable  transverse  strains  or  shocks, 
wrought  iron  would  be  a  better  material  than  cast  iron. 

490.  Construction. — Instead  of  the  soffit  being  a  continu- 
ous surface,  as  in  the  masonry  arch,  it  is  formed,  in  the  iron 
arch,  of  curved  iron  beams  placed  side  by  side  at  suitable 
distances  apart,  and  bound  together  by  lateral  bracing.     This 
lateral  bracing  binding  the  ribs  together,  the  proper   abut- 
ting of  the  ends  of  the  ribs,  and  the  fastening  of  them  upon 
the  bed-plates  or  skew-backs  of  the  abutments,  form  the  most 
important  part  of  the  construction. 

The  ribs  are  generally  made  in  segments,  the  joints  being 
in  the  direction  of  the  radii  of  curvature  of  the  under  surface 
of  the  rib.  To  guard  against  any  possibility  of  accident,  the 
segments  are  bolted  together  at  the  joints,  forming  in  this 
way  a  continuous  curved  beam. 

The  form  of  the  under  surface  of  the  rib  is  either  parabolic 
or  circular,  more  generally  the  latter.  The  depth  of  the  rib 
is  taken  ordinarily  at  about  -fath  of  the  span. 


J I 


[ 

1     1 

1 

1 

1  ,  1 

I 

1 

1 

1 

1 

1 

1 

1     1 

FIG.  194. 

The  rib  may  be  solid,  having  a  cross-section  of  the  usual 
x-shape,  the  upper  and  lower  flanges  being  equal ;  or  it  may 
be  tubular ;  or  it  may  be  open-work,  similar  to  a  truss  in  which 
the  chords  are  curved. 

The  first  is  the  usual  form.  The  other  forms  have  been 
are  frequently  used,  but  require  no  particular  description. 


ARCHED   BRIDGES.  371 

Whatever  be  the  form  of  cross-section  of  the  rib,  it  is  usual 
to  place  above  the  crown  a  horizontal  beam,  generally  of 
wrought  iron,  suitably  stiffened  by  covering  plates  and  angle 
irons.  (Fig.  194.) 

The  connection  of  this  beam  with  the  curved  rib  is  made 
by  a  truss-work,  called  the  spandrel  filling,  as  shown  in  the 
figure. 

On  the  horizontal  beams  the  roadway  is  placed. 

491.  Expansion  and  contraction. — The  rib  is  frequently 
hinged  at  the  crown  and  ends,  and  sometimes  at  the  ends 
only,  to  provide  for  the  expansion   and  contraction  of  the 
metals  produced  by  changes  of  temperature. 

It  is  a  matter  of  doubt  whether  anything  is  gained  by  this 
provision,  as  the  friction  arising  from  the  great  pressure  on 
the  joint  probably  prevents  the  motion  of  rotation  necessary 
to  relieve  the  arch  from  the  increased  strain. 

492.  Arched  bridges  of  steel. — Bridges   of    this   class, 
made  of  steel,  do  not  differ  in  principle  from  those  in  iron. 
The  most  noted  example  of  the  steel  arch  is  that  used  in  the 
St.  Louis  and  Illinois  Bridge,  across  the  Mississippi  River, 
at  St.  Louis,  Missouri. 

In  this  bridge,  the  portion  which  corresponds,  in  the  previ- 
ous descriptions,  to  the  rib,  is  composed  of  two  tubular  steel 
ribs  placed  directly  one  over  the  other  and  connected  by  a 
truss-work. 

The  segments  of  each  of  the  tubular  ribs  are  straight 
throughout  their  length,  instead  of  being  curved.  The  ends 
of  each  segment  are  planed  off  in  the  direction  of  the  radius 
of  curvature,  and  abut  against  the  ends  of  the  adjacent  seg- 
ment, to  which  they  are  joined  and  fastened.  In  this  way 
the  tube  is  made  continuous ;  but  instead  of  being  curved,  it 
is  polygonal,  as  in  the  case  of  the  bowstring  girder.  The 
tubes  are  connected  by  a  truss- work,  and  the  whole  forms  a 
rib  of  the  third  class. 

493.  Bads'  patent  arch  bridge. — Captain  Eads,  the  en- 
gineer of  the  St.  Louis  Bridge,  has  patented  an  arch  bridge, 
the  principle  of  which  is  shown  in  Fig.  195. 

This  arch  is  hinged  at  the  crown,  C,  and  springing  lines, 
A  and  B,  to  provide  for  the  expansion  and  contraction  of  the 
metal  used  in  its  construction.  This  arrangement  of  hinging 
the  arch  at  the  crown  reduces  the  construction  to  that  of  two 
inclined  beams  resting  against  each  other  at  C.  Each  beam 
is  a  truss  belonging  to  the  triangular  system  and  having  curved 
chords. 

The  line,  A  C  B,  is  the  arc  of  a  parabola,  whose  vertex  if 


372 


CIVIL  ENGUNEEBING. 


at  C.  The  lines,  ADC  and  C  E  B,  are  also  arcs  of  parabolas. 
The  maximum  depth  of  either  truss  must  not  exceed  one-half 
the  rise  of  A  C  B. 


FIG.  195. 

494.  Cases  in  which  the  arch  may  be  preferred  to  the 

truss. 

The  arch  will  usually  be  found  to  be  a  less  expensive  struc- 
ture than  the  truss,  when  the  banks  are  of  rock  forming  good 
natural  abutments. 

It  will  oftentimes  be  more  economically  employed  where  a 
deep  valley  is  to  be  spanned  and  where  high  arches  can  be 
used. 

It  is  to  be  preferred  when  the  roadway  is  a  very  heavy  one, 
as  in  the  case  of  a  macadamized,  or  similar  covering. 

It  is  frequently  selected  in  preference  to  a  truss,  from 
architectural  considerations. 


CHAPTER  XVII. 


IV.  SUSPENSION  BRIDGES. 


495.  A  suspension  bridge  is  one  in  which  the  roadway 
over  the  stream  or  space  to  be  crossed  is  suspended  from 
chains  or  wire  ropes.  The  chains  or  wire  ropes  pass  over 
towers,  the  ends  of  the  chains  being  securely  fastened  or 
"anchored"  ia  masonry  at  some  distance  behind  and  below 
the  towers.  The  roadway,  usually  of  wooden  planking,  is 


SUSPENSION   BRIDGES. 


373 


supported  by  suspending  rods  placed  at  regular  distances 
along  the  chains.     (Fig.  196.) 


FIG.  196. 

Suspension  bridges  are  used  principally  for  spans  so  great 
that  they  can  not  be  crossed  by  arches  or  truss-work  at  a 
reasonable  cost.  Sometimes  they  are  used,  where  the  span  is 
not  very  great,  as  a  roadway  only  for  foot  passengers,  especi- 
ally over  high-banked  rivers,  ravines,  and  similar  places  where 
the  cost  of  a  bridge  of  the  other  kinds  would  be  out  of  pro- 
portion to  the  service  required. 

496.  A  suspension  bridge  consists  of  the  towers  or  piers, 
over  which  the  main  chains  or  cables  pass ;  the  anchorages, 
to  which  the  ends  of  the  cables  are  attached ;  the  main  chains 
or  cables,  from  which  the  roadway  is  suspended  ;  the  sus- 
pending rods  or  chains,  which  connect  the  roadway  with 
the  main  chains ;  and  the  roadway. 

497.  Towers. — The  towers,  frequently  termed  piers,  are 
made  generally  of  masonry,  although  iron  has  sometimes  been 
used.     The  particular  form  of  the  towers  will  depend  in  a 
measure  upon  the  locality  and  the  character  of  the  surround- 
ings.    Their  dimensions  will  depend 

upon  their  height  and  the  amount 
of  strains  which  they  will  have  to 
resist. 

Their  construction  will  be  governed 
by  the  rules  already  given  for  the 
careful  construction  of  masonry. 

A  cast-iron  saddle  on  rollers,  to  allow 
of  free  motion  in  the  direction  of  the 
length  of  the  main  chains,  is  placed  FIG.  197. 

on  each  tower.     (Fig.  197.) 

The  main  chains  may  be  fastened  to  these  saddles,  but  thej 
are  generally  passed  over  them. 


374  CIVIL   ENGINEERING. 

The  strains  on  the  towers  are  produced  by  the  vertical  and 
horizontal  components  of  the  tensions  in  the  cables. 

The  tower  must  be  built  expressly  to  resist  the  crushing 
forces  due  to  this  vertical  component  of  the  tension  and  the 
weight  of  the  masonry. 

If  the  saddle  was  not  free  to  move,  the  horizontal  force 
tending  to  push  the  tower  over  would  be  equal  to  the  differ- 
ence of  the  horizontal  components  of  the  tension  in  the  two 
brandies  of  the  main  chain.  But  since  the  saddle,  by  means 
of  the  rollers,  is  free  to  move,  the  horizontal  force  acting  at 
the  top  of  the  tower  must  be  less  than  the  friction  of  the 
rollers. 

498.  Anchorage. — If  the  shore  or  bank  be  of  rock,  a  ver- 
tical passage  should  be  excavated   and  a  strong  iron  plate 
placed  in  the  bottom  and  firmly  imbedded  in  the  sides  of  the 
passage.     Through  this  plate  the  ends  of  the  main  chains  are 
passed  and  firmly  secured  on   the  under  side.     After   the 
chains  are  put  in  place  the  passage  should  be  filled  with  con- 
crete and  masonry. 

If  the  rock  is  not  suitable,  a  heavy  mass  of  masonry  should 
be  built  of  large  blocks  of  cut  stone,  well  bonded  together 
for  this  purpose.  In  this  case  it  is  advisable  to  construct  a 
passage  way,  so  that  the  chains  and  the  fastenings  may  be 
examined  at  any  time.  This  mass  of  masonry,  or  the  natural 
rock  to  which  the  ends  of  the  chain  are  fastened,  is  frequently 
called  the  abutment.  Its  stability  must  be  greater  than  the 
tension  of  the  chains.  The  principles  of  its  stability  are 
precisely  the  same  as  those  for  the  abutment  of  an  arch ;  its 
weight  and  thickness  must  be  sufficient  to  prevent  its  being 
overturned ;  and  its  centre  of  resistance  must  be  within  safe 
limits. 

499.  Main  chains   or  cables. — These  may  be  made  of 
iron  bars,  connected  by  eye-bar  and  pin  joints;  of  iron  links, 
as  in  common  chains ;  of  hoop  or  strap  iron ;  of  ropes  or 
cables  of  wire,  and  in  some  cases  of  vegetable  fibre,  as  hemp, 
flax,  or  bark.     When   of   ropes  or  strap  iron   they  are  of 
uniform  cross-section ;  when  of  links  they  may  have  variable 
cross-sections. 

The  smallest  number  of  cables  in  a  suspension  bridge  is 
two,  one  to  support  each  side  of  the  roadway.  Generally 
more  than  two  cables  are  used,  since,  for  the  same  amount  of 
material,  they  offer  at  least  the  same  resistance,  are  more 
accurately  manufactured,  are  liable  to  less  danger  of  accident, 
and  can  be  more  easily  put  in  place  and  replaced  than  a  single 
chain  of  an  equal  amount  of  material. 


SUSPENSION   BEIDGE8.  375 

Discussions  have  arisen  as  to  the  respective  advantages 
possessed  by  the  chain  and  wire  cables,  some  engineers  pre- 
ferring the  former  to  the  latter,  and  the  reverse.  The  wire 
cable  is  generally  adopted  in  the  United  States. 

The  wire  cable  is  composed  of  wires,  generally  from  £th 
to  £th  of  an  inch  in  diameter,  which  are  brought  into  a  cylin- 
drical shape  by  a  spiral  wrapping  of  wire.  Great  care  is 
taken  to  give  to  each  wire  in  the  cable  the  same  degree  of 
tension. 

The  iron  wires  are  coated  with  varnish  before  they  are 
bound  up  into  the  cable,  and  when  the  cable  is  completed 
the  usual  precautions  are  taken,  as  in  other  iron-work,  to 
protect  it  from  rust  and  the  action  of  the  weather. 

If  the  load  placed  on  a  cable  be  a  direct  function  of  its 
length,  the  curve  assumed  by  the  mean  fibre  of  the  cable  will 
be  a  catenary.  If  it  be  a  direct  function  of  the  span,  it  will 
be  a  parabola.  But  the  weight  resting  on  the  main  chains  is 
neither  a  direct  function  of  the  length  of  the  cable,  nor  of 
the  span,  but  a  function  of  both.  The  curve  is  therefore 
neither  a  catenary  nor  a  parabola.  But  since  the  roadway, 
which  forms  the  principal  part  of  the  load,  is  distributed  very 
nearly  uniformly  over  the  span,  the  curve  approaches  more 
nearly  the  parabola  and  in  practice  is  regarded  as  such  a 
curve. 

Knowing  the  horizontal  distance  between  the  tops  of  the 
towel's  and  the  deflection,  the  corresponding  length  of  the 
cable  between  the  two  points  of  support  may  be  obtained  by 
the  operation  of  rectifying  the  curve  of  a  parabola.  (Church's 
Integral  Calculus,  Art.  235.)  The  length  obtained  by  this 
method  will  be  expressed  in  terms  containing  logarithmic 
functions.  For  this  reason  approximate  formulas  are  made 
which  will  give  the  length,  in  most  cases,  near  enough  for 
practical  purposes.  Rankine  gives  the  following  approxi- 
mate value  for  the  length  of  a  parabolic  arc : 

v2 
s  =  x  +  f  ^-      (nearly).    .    .     (162). 

Where  the  cable  is  to  have  a  constant  cross-section  through- 
out, the  area  of  this  section  must  be  proportioned  to  the 
greatest  tension  upon  the  cable.  This  tension  is  greatest  at 
the  points  of  support  when  they  are  of  the  same  height,  or 
at  the  highest  point  when  the  heights  are  unequal. 

If  the  main  chain  is  made  of  bars  or  links,  it  may  be  pro- 
portioned to  form  a  chain  of  uniform  strength,  in  which  case 
the  cross-sections  will  be  made  to  vary  from  the  lowest  point 


376  CIVIL   ENGINEERING. 

to  the  highest,  increasing  in  area  of  cross-section  as  the  strain 
of  tension  increases.  The  horizontal  component,  or  tension 
of  the  lowest  point,  is  dependent  upon  the  parameter  of  the 
curve.  It  therefore  follows  that  for  the  same  curve  and  the 
same  load  on  the  unit  of  length  throughout,  the  horizontal 
component  is  the  same  for  a  bridge  of  a  span  of  ten  as  for 
one  of  a  thousand  feet.  And  it  is  also  plain  that  the  wider 
the  span,  the  deflection  remaining  constant,  the  greater  will 
be  the  tension  on  the  cable,  and  the  reverse. 

500.  Suspending    chains. — The    roadway    is    suspended 
from  the  cables  by  wire  ropes  or  iron  rods,  which  are  placed  at 
equal  distances  along  the  cable,  for  the  purpose  of  distributing 
the  load  as  uniformly  as  possible  over  the  cables. 

If  the  cables  are  composed  of  links  or  bars,  the  suspending 
rods  may  be  attached  directly  to  them.  If  of  rope,  either  of 
wire  or  of  vegetable  material,  the  suspension  rod  is  attached 
to  a  collar  of  "iron  of  suitable  shape  bent  around  the  cable,  or 
to  a  saddle-piece  resting  on  it. 

Where  there  are  two  cables,  care  must  be  taken  to  dis- 
tribute the  load  upon  the  cables  according  to  their  degree  of 
strength. 

In  the  Hungerford  Suspension  Bridge  the  method  adopted 
was  as  follows :  The  suspension  rod,  A  (Fig.  198),  was  at- 
tached to  a  triangular  plate,  B, 
which  hung  by  the  rods,  C  and 
D,  from  the  main  chain,  E  and 
F.  By  this  arrangement  half 
of  the  load  on  the  rod,  A,  was 
supported  by  each  of  the  main 
chains,  E  and  F. 

The    suspending  rods   may 
be   vertical   or   inclined.      In 
recent  constructions  they  are 
FIG.  198.  frequently   inclined    inwards, 

for  the  purpose  of  giving  ad- 
ditional stiffness  to  the  framing.  The  cross-section  of  the 
rod  is  constant,  and  is  determined  by  the  amount  of  strain  on 
the  upper  section. 

501.  Roadway. — The   roadway   in  its  construction  does 
not  differ  in  principle  from  that  used  for   other  forms  of 
bridges.     The  roadway  bearers  are  supported  by  the  suspen- 
sion rods.     On  the  bearers  are  laid  longitudinal  joists,  and  on 
them  the  planking,  or  the  planking  is  laid  directly  on  the  road- 
way bearers.     The  latter  are  stiffened  by  diagonal  ties  of  iron 
placed  horizontally  between  each  pair  of  roadway  bearers. 


SUSPENSION   BRIDGES. 


377 


502.  Oscillations. — Suspension  bridges,  from  the  nature 
of  their  construction,  are  wanting  in-  stiffness,  and  hence  are 
peculiarly  liable  to  both  vertical  and  horizontal  oscillations, 
caused  by  moving  loads,  action  of  winds,  etc. 

These  oscillations  cannot  be  entirely  prevented,  but  their 
effect  may  be  reduced  so  as  to  be  almost  harmless. 

When  the  banks  will  admit  of  it,  guy-ropes  of  wire  may 
be  attached  to  the  roadway  and  fastened  to  points  of  the 
bank  beneath  the  bridge.  The  guy-ropes  directly  under  the 
bridge  will  be  the  most  effective  in  resisting  the  vertical 
oscillations;  those  oblique  to  the  bridge,  for  resisting  the 
horizontal. 

The  elder  Brunei  fastened  the  roadway  to  a  set  of  chains, 
whose  curve  was  the  reverse  of  that  of  the  main  chains.  The 
reversed  chains  had  a  cross-section  of  about  one-third  of  the 
main  chains,  and  preserved  the  shape  of  the  roadway  under  a 
movable  load  even  better  than  the  guys. 

Engineers  have  made  many  efforts  to  provide  for  this  want 
of  stiffness  in  suspension  bridges  and  to  fit  them  for  railroad 
uses. 

A  heavy  moving  load  coming  on  a  suspension  bridge, 
when  at  a  point,  as  M  (Fig.  199),  causes  the  roadway  and 
cables  to  assume  positions  similar  to  those  indicated  by  the 


FIG.  199. 

dotted  lines  in  the  figure.  To  prevent  this  deformation,  the 
cables  are  fastened  at  the  points  of  greatest  change  by  chains, 
A  E  and  B  F,  attached  to  the  piers.  These  are  known  as 
Ordish's  chains. 

Roebling  effected  the  same  result  by  fastening  these  points 
of  change  in  the  roadway  to  the  top  of  the  towers,  by  the 
lines,  Da,  Db,  etc.,  as  shown  in  Fig.  200. 

It  is  agreed  at  the  present  time  that  the  best  method  of 
increasing  the  stiffness  of  a  suspension  bridge  is  to  use,  in 
addition  to  the  chains  just  named,  trussed  parapets  on  each 
side  of  the  roadway.  These  parapets  form  two  open-built 
beams,  strongly  connected  and  braced  by  the  roadway,  and 


378 


CIVIL   ENGINEERING. 


supported  at  intermediate  points  by  the  attachments  to  the 
main  chains.  Each  end  of  the  roadway  is  firmly  secured  to 
the  base  of  the  tower. 


FIG.  200. 


The  objection  to  this  method  is  the  increase  of  the  weight 
placed  upon  the  main  chains. 

503.  Niagara  Suspension  Bridge, — This  bridge  was 
planned  and  constructed  by  Roebling,  and  illustrates  the 
method  of  stiffening  just  described. 

The  bridge  affords  a  passage-way  over  the  Niagara  River,  a 
short  distance  below  the  Falls,  both  for  a  railroad  and  a  com- 
mon road.  It  consists  of  two  platforms  (Fig.  201),  one  above 


Die" 


FIG.  201. 


the  other,  and  about  fifteen  feet  apart ;  the  upper  is  for  the 
railroad  track,  and  the  lower,  B,  is  for  the  common  road.  The 
platforms  are  connected  by  a  lattice  truss-work,  C,  C,  on  each 
Bide,  which  serves  to  increase  its  stiffness.  The  whole  bridge 
is  suspended  by  four  main  wire  cables,  F,  F,  F',  F',  the  upper 


NIAGARA    SUSPENSION   BRIDGE. 


379 


two  being  connected  with  the  upper  platform,  and  the  lower 
two  with  the  lower  platform. 

Each  platform  consists  of  a  series  of  roadway  bearers  in 
pairs ;  the  lower  covered  by  two  thicknesses  of  flooring- 
plank,  the  upper  by  one  thickness ;  the  portion  of  the  latter 
immediately  under  the  railroad  track  having  a  thickness  of 
four  inches,  and  the  remainder  on  each  side  but  two  inches. 

The  roadway  bearers  and  flooring  of  the  upper  platform 
are  clamped  between  four  solid-built  beams ;  two  above  the 
flooring,  which  rest  on  cross  supports ;  and  two,  correspond- 
ing to  those  above,  below  the  roadway  bearers ;  the  upper 
and  lower  corresponding  beams,  with  longitudinal  braces  in 


pairs  between  the  roadway  bearers  and  resting  on  the  lower 
beams,  being  firmly  connected  by  screw-bolts.  The  rails  are 
laid  upon  the  top  beams,  forming  the  railroad  track,  A.  A 
parapet,  D,  D,  of  the  form  of  the  Howe  truss  is  placed  on 
each  side. 

The  lattice-work,  C,  C,  which  connects  the  upper  and 
lower  platforms,  consists  of  vertical  posts  in  pairs  (Figs.  202), 
and  ot  diagonal  wrought-iron  rods,  T,  T.  The  rods  pas* 


380 


CIVIL   ENGINEERING. 


§ 


through  cast-iron  plates  fastened  above  the  roadway  bearers 
of  the  upper  platform,  and  below  those  of  the  lower,  and  are 
brought  to  a  proper  bearing  by  nuts  and  screws  on  each  end. 
A  horizontal  rail  of  timber  is  placed  between  the  posts  of  the 
lattices  at  their  middle,  to  prevent  flexure. 

The  towers  (Fig.  203)  are 
four  obelisk-shaped  pillars,  each 
sixty  feet  high,  with  a  square 
base  of  fifteen  feet  on  a  side, 
and  one  of  eight  feet  at  the 
top. 

The  height  of  the  pedestals  on 
the  Canada  side  is  eighteen  feet, 
and  on  the  United  States  twenty- 
eight.  An  arch,  C,  connectg 
the  two  pedestals,  under  which 
is  a  carriage-way,  D,  for  com- 
municating with  the  lower  plat- 
form. 

B     \^     ft    ^1       |s  The   main   cables    pass   over 

1  I       I*  saddles  on  rollers  placed  on  tops 

....XQL...L.../A'.C....l — 1 of  the  towers,  and  are  fastened 

FIG.  203.  at  their  ends  (Fig.  204)  to  chains 

made  of  iron  bars  attached  to  an 

anchoring  plate,  D,  of  iron,  firmly  secured  in  an  anchorage  of 
rock,  B,  and  a  mass  of  masonry,  A. 


20' 


FIG.  204. 

The  upper  cables  are  drawn  in  towards  the  axis  of  the 
bridge  to  reduce  the  amount  of  horizontal  oscillations. 


MOVABLE    BBHKJE8.  381 

The  following  are  some  of  its  principal  dimensions  : 

Span  of  the  cables,  821^  feet. 

Deflection  of  upper  cables  (mean  temperature),  54  feet. 

Deflection  of  lower  cables      "  "  64  feet. 

Length  of  upper  cables  u  "        1,193  feet. 

Length  of  lower  cables  "  "        1,261  feet. 

Ultimate  strength  of  the  four  cables,  12,000  tons. 

Permanent  weight  supported  by  the  cables,  1,000  tons. 

Tensile  stress  in  the  four  cables,  1,810  tons. 

Height  of  railroad  track  above  mean  stage  of  water,  245 
feet. 

After  a  constant  use  of  over  25  years,  this  bridge  had  its 
anchorages  reinforced  (1877-8),  and  its  superstructure  re- 
newed (1880)  by  substituting  iron  and  steel  for  the  wood. 
(Transactions  of  the  Am.  Society  of  Civil  Engineers,  July, 
1881.) 

504.  East  River  Suspension  Bridge. — This  bridge 
connects  the  cities  of  New  York  and  Brooklyn,  and  was 
thrown  open  to  the  public  in  1883.  Is  was*  planned  by 
Koebling  and  completed  under  the  direction  of  his  son,  Col. 
W.  A.  Roebling.  Some  of  its  dimensions  are  as  follows  : 

Length  of  span  over  the  river,  1,595£  feet. 

Total  length  of  bridge,  5,989  feet. 

Height  of  bridge  at  the  centre  over  the  river,  135  feet. 

The  ultimate  strength  of  the  cables  is  49,200  tons,  with  a 
tensile  stress  of  11,700  tons  produced  by  an  estimated  load 
of  8,120  tons. 


CHAPTEK  XVIIL 

V.  MOVABLE  AND  AQUEDUCT  BRIDGES. 

505.  Movable  bridges. — In  bridges  over  navigable  rivers 
it  is  often  necessary  that  one  or  more  spans  be  made  to  move 
aside  to  allow  of  the  passage  of  vessels.  The  term,  movable 
bridge,  is  therefore  applied  to  any  arrangement,  whatever 
be  its  nature,  by  means  of  which  the  roadway  can  at  pleasure 
be  made  continuous  or  broken,  between  two  points  of  a  per- 
manent bridge,  or  over  a  water-way.  The  methods  used  to 
effect  this  result  are  various. 

They  may  be  classed  under  five  heads : 


382  CIVIL   ENGINEERING. 

The  passage  may  be  opened  or  closed ;  1,  by  turning  a 
portion  of  the  bridge  around  a  vertical  axis  ;  2,  by  turning 
it  around  a  horizontal  axis ;  3,  by  making  it  roll  forwards 
and  backwards  in  a  line  with  the  bridge ;  4,  by  lifting  it 
vertically  above  the  passage  ;  and  5,  by  floating  it  from  and 
into  place  upon  the  water. 

506.  I.  By  turning  around  a  vertical  axis. — The  term, 
swing-bridge,  is  generally  applied  to  a  bridge  which  turns 
about  a  vertical  axis.     This  form  of  bridge  is  the  one  most 
generally  used  when  the  opening  is  of  any  size.     If  two  open- 
ings are  required,  the  bridge  rests  upon  a  masonry  pier,  which 
is  placed  midway  between  the  openings,  and  which  supports 
a  circular  plate,  whose  diameter  is  equal,  or  nearly  equal,  to 
the  breadth  of  the  bridge.     This  plate  has  in  the  centre  a 
pivot  surrounded  by  a  circular  track  with  rollers.     On  this 
pivot  and  rollers  the  bridge  is  revolved  horizontally,  being 
turned  by  suitable  machinery. 

If  only  one  opening  is  required,  the  abutment  is  generally 
used  to  support  the  mechanism  for  turning  the  bridge,  care 
being  taken  to  place  the  pivot  far  enough  back  from  the  face 
of  the  abutment  so  that  the  bridge,  when  open,  shall  not  pro- 
ject beyond  it. 

In  calculating  the  strains  on  the  parts  of  such  a  bridge,  the 
latter  is  usually  considered  when  open,  as  composed  of  two 
cantilevers,  each  loaded  with  its  own  weight ;  when  closed,  as 
a  bridge  of  two  spans. 

507.  II.  By  turning  around  a  horizontal  axis. — Where 
the  width  of  the  opening  is  small,  the  moving  portion  of  the 
bridge,  which  may  be  in  one  or  two  pieces,  is  lifted  by  chains 
attached  to  the  extremities,  the  operation  of  lifting  being  as- 
sisted by  counterpoises  connected  with  the  mechanism  used. 
One  of  the  simplest  counterpoises  is  a  lever  revolving  on  a 
horizontal  axis  above  the  bridge,  one  end  of  the  lever  being 
connected  with  the  movable  end  of  the  bridge  by  a  chain,  the 
other  being  weighted  and  connected  with  the  mechanism  by 
which  the  bridge  is  lifted. 

508.  III.  By  moving  a  portion  of  the  bridge  forward 
and  backward  in  a  line  with  its  axis. — Bridges  of  this 
kind  are  placed  upon  fixed  rollers,  so  that  they  can  be  moved 
forward  or  backward,  to  interrupt  or  open  the  communication 
across  the  water-way.     The  part  of  the  bridge  that  rests  upon 
the  rollers,  when  the  passage  is  closed,  forms  a  counterpoise 
to  the  other.     The  mechanism  usually  employed  for  moving 
these  bridges  consists  of  tooth- work,  and  may  be  so  arranged 
that  it  can  be  worked  by  one  or  more  persons  standing  on  the 


AQUEDUCT  BRIDGES.  383 

bridge.  Instead  of  fixed  rolleis  turning  on  axles,  iron  balls 
resting  in  a  grooved  roller- way  may  be  used,  a  similar  roller- 
way  being  affixed  to  the  frame-work  beneath. 

Bridges  of  this  class  are  known  as  rolling  bridges. 

509.  TV.  By  lifting. — In  small  bridges,  like  those  over 
canals,  the  bridge  is  sometimes  hung  by  the  four  corners  to 
chains  which  pass  over  pulleys  and  have  counterpoises  at  the 
other  ends.     A  slight  force  applied  to  it  raises  the  bridge 
to  the  required  height,  allowing  the  boats  to  pass  under  the 
bridge. 

510.  Y.  By  floating. — A  movable  bridge  of  this  kind  may 
be  made  by  placing  a  platform  to  form  a  roadway  upon  a 
boat  or  a  water-tight  box  of  a  suitable  shape.     This  bridge  is 
placed  in  or  withdrawn  from  the  water-way,  as  circumstances 
may  require. 

A  bridge  of  this  character  cannot  be  conveniently  used  in 
tidal  waters,  except  at  certain  stages  of  the  water.  It  may 
be  employed  with  advantage  on  canals  in  positions  where  a 
fixed  bridge  could  not  be  placed,  in  which  case  a  recess  in 
the  side  or  the  canal  is  made  to  receive  the  bridge  when  the 
passage-way  is  opened. 

511.  The  general  term,  draw-bridge,  is  applied  to  all  these 
movable  bridges,  although  technically  the  term  is  confined 
to  bridges  of  the  second  class,  or  those  revolving  around  a 
horizontal  axis. 

Movable  bridges  are  either  simple  bridges  or  made  of 
truss-work  belonging  to  one  of  the  three  systems  already 
named. 

The  objections  to  using  either  a  tubular,  an  arched,  or  a 
suspension  bridge  for  a  movable  bridge  are  apparent.  Where 
either  of  these  classes  is  used,  the  passage-way  can  only  be 
kept  open  by  constructing  the  bridge  so  that  a  vessel  can  pass 
beneath  it. 

512.  Aqueduct    bridges. — In   aqueducts    for    supplying 
a  city  with  water,  the  volume  of  water  conveyed  is  com- 
paratively small,  and  the  aqueduct  bridge  will   present  no 
peculiar  difficulties  except  those  of  a  water-tight  channel. 
The   latter   may  be   made  either  of  masonry,   or  of   cast- 
iron  pipes,  according  to   the   quantity  of  water  to  be  de- 
livered.    If  formed  of  masonry,  the  sides  and  bottom  of 
the   channel   should   be  laid  in   the   most   careful   manner 
with  hydraulic  cement,  and  the  surface  in  contact  with  the 
water  should   receive  a  coating  of   the  same  material,  par- 
ticularly if  the  stone  or  brick  used  be  of  a  porous  nature. 
This  part  of  the  structure  should  not  be  commenced  until  the 


384:  CIVIL   ENGINEEKING. 

arches  have  been  uncentered  and  the  heavier  parts  of  the 
structure  have  been  carried  up  and  have  had  time  to  settle. 
The  interior  spandrel-filling,  to  the  level  of  the  masonry 
which  forms  the  bottom  of  the  water-way,  may  either  be 
formed  of  solid  material,  of  good  rubble  laid  in  , hydraulic 
cement,  or  of  concrete ;  or  a  system  of  interior  walls,  like 
those  used  in  common  bridges  for  the  support  of  the  roadway, 
may  be  used  to  sustain  the  masonry  of  the  water-way. 

In  aqueduct  bridges  of  masonry,  supporting  a  navigable 
canal,  the  volume  of  water  is  much  greater  than  in  the 
preceding  case,  and  every  precaution  should  be  taken  to 
procure  great  solidity,  and  to  secure  the  structure  from  acci- 
dents. 

Segmental  arches  of  medium  span  will  generally  be  found 
most  suitable  for  works  of  this  character.  The  section  of 
the  water-way  is  generally  of  a  trapezoidal  form,  the  bot- 
tom line  being  horizontal.  For  economy,  the  water-way  is 
usually  made  wide  enough  for  one  boat  only ;  on  one  side  is 
a  tow-path  for  the  horses,  and  on  the  other  a  narrow  foot- 
path. 

The  principle  of  the  suspension  bridge  is  well  adapted  to 
aqueduct  bridges,  because,  as  each  boat  displaces  its  own 
weight  of  water,  the  only  moving  load  is  the  passage  of  men 
and  horses  along  the  tow-path. 


CHAPTER  XIX. 
BEIDGE  CONSTRUCTION. 

513.  Before  a  bridge  can  be  constructed  there  are  three 
things  to  be  considered,  viz.;  1st,  the  site ;  2d,  the  water-way ; 
3d,  the  design  or  plan. 

Before  a  bridge  can  be  designed  a  thorough  knowledge  of 
the  site,  the  amount  of  water-way,  and  the  particular  service 
required  of  the  bridge,  must  all  be  known. 

514.  Site. — The  site  may  already  be  determined,  and  it 
may  not  be  in  the  power  of  the  engineer  to  change  it.     If  it 
is  in  his  power  to  locate  the  site  within  certain  limits,  he 
will  select  the  locality  which  offers  the  most  security  to  the 


BRIDGE    CONSTRUCTION.  385 

foundations  and  which  requires   the  least  expense   to   be 
incurred  in  their  construction  and  in  that  of  the  bridge. 

in  many  cases  it  is  a  matter  of  indifference  where  the 
stream  is  crossed,  but  a  careful  survey  of  the  proposed  site 
should  always  be  made,  accompanied  by  borings.  The 
object  of  this  survey  is  to  ascertain  thoroughly  the  natural 
features  of  the  surface,  the  nature  of  the  subsoil  of  the  bed 
and  banks  of  the  water-course,  and  the  character  of  the 
water-course  at  its  different  phases  of  high  and  low  water, 
and  of  freshets.  This  information  should  be  embodied  in  a 
topographical  map;  in  cross  and  longitudinal  sections  of  the 
water-course  and  the  substrata  of  its  bed  and  banks ;  and  in 
a  descriptive  memoir  which,  besides  the  usual  state  of  the 
water-course,  should  exhibit  an  account  of  its  changes,  occa- 
sioned either  by  permanent  or  by  accidental  causes,  as  from 
the  effects  of  extraordinary  freshets,  or  from  the  construction 
of  bridges,  dams,  and  other  artificial  changes  either  in  the 
bed  or  banks. 

Having  obtained  a  thorough  knowledge  of  the  site,  the 
two  most  essential  points  next  to  be  considered  are  to  adapt 
the  proposed  structure  to  the  locality,  so  that  a  sufficient 
water-way  shall  be  left  both  for  navigable  purposes  and  for 
the  free  discharge  of  the  water  accumulated  during  high 
freshets ;  and  to  adopt  such  a  system  of  foundations  as  will 
ensure  the  safety  of  the  structure. 

515.  Water-way. — When  the  natural  water-way  of  a 
river  is  obstructed  by  any  artificial  means,  the  contraction,  if 
considerable,  will  cause  the  water,  above  the  point  where  the 
obstruction  is  placed,  to  rise  higher  than  the  level  of  that 
below  it.  This  difference  of  level  is  accompanied  by  an  in- 
crease of  velocity  in  the  current  of  the  river  at  this  place. 
This  damming  of  the  water  above  the  obstruction,  and  in- 
crease of  velocity  in  the  current  between  the  level  above  and 
the  one  below  the  obstruction,  may,  during  heavy  freshets, 
cause  overflowing  of  the  banks ;  may  endanger,  if  not 
entirely  suspend,  navigation  during  the  seasons  of  freshets ; 
and  expose  any  structure  which,  like  a  bridge,  forms  the 
obstruction,  to  ruin,  from  the  increased  action  of  the  current 
upon  the  soil  around  its  foundations. 

If  on  the  contrary,  the  natural  water-way  is  enlarged  at 
the  point  where  the  structure  is  placed,  with  the  view  of  pre- 
venting these  consequences,  the  velocity  of  the  current 
during  the  ordinary  stages  of  the  water  will  be  decreased, 
and  this  will  occasion  deposits  to  be  formed  which,  by  gradu- 
ally filling  up  the  bed  of  the  stream,  might  prove,  on  a  sudden 


386  CIVIL   ENGINEERING. 

rise  of  the  water,  a  more  serious  obstruction  than  the  struc- 
ture itself;  particularly  if  the  main  body  of  the  water 
should  happen  to  be  diverted  by  the  deposit  from  its 
ordinary  course,  and  form  new  channels  of  greater  depth 
near  the  foundations  of  the  structure. 

For  these  reasons,  the  water-way  to  be  left  after  the  bridge 
is  built  should  be  so  regulated  that  no  considerable  change 
shall  be  occasioned  in  the  velocity  of  the  current  through  it 
during  the  most  unfavorable  stages  of  the  water. 

The  beds  of  rivers  are  constantly  undergoing  change,  the 
amount  and  nature  of  which  depend,  upon  the  kind  of  soil  oi 
which  they  are  composed,  and  the  velocity  of  the  current. 

516.  The  following  table  shows,  on  the  authority  of  Du 
Buat,  the  greatest  velocities  of  the  current  close  to  the  bed 
without  injury  to  or  displacement  of  the  material  of  which  it 
is  composed : 

Soft  clay 0.25  feet  per  second. 

Fine  sand 0.50         "  " 

Coarse  sand  and  fine  gravel. . .   0.70         "  " 

Gravel,  ordinary 1.00 

Coarse  gravel,  1  in.  in  diameter  2.25 

Pebbles,  1 J-  in.  in  diameter.  . .   3.33         "  " 

Heavy  shingle 4.00         "  " 

Soft  rock,  brick,  etc 4.50         "  " 

T?    i  \  6.00         «  « 

Rock jand  greater. 

Knowing  the  material  of  which  the  bed  of  the  river  at 
the  site  is  composed,  and  regulating  the  water-way  so  that 
the  velocity  of  the  current  close  to  the  bottom  after  the 
bridge  has  been  erected,  during  the  heaviest  freshets  shall 
not  exceed  the  limit  of  safety  or  disturbance  of  the  material 
forming  the  bed,  the  stability  of  the  foundations  is  assured. 
If  the  velocity  should  exceed  the  limits  here  given,  precau- 
tions must  be  taken  to  protect  the  foundations,  as  heretofore 
described. 

517.  Velocity. — The  velocity  of  a  current  depends  upon 
the  slope  of  the  bed.     Since  the  particles  of  water  in  contact 
with  the  earth  of  the  sides  and  bottom  of  the  stream  are 
retarded  by  friction,  it  follows  that  in  any  cross-section  the 
velocity  of  the  particles  in  the  centre  differs  from  those  at 
the  bottom  and  on  the  sides.     In  ordinary  cases  it  is  suffi- 
ciently exact  to  take  the  least,  mean,  and  greatest  velocities 
as  being  nearly  in  the  proportions  of  3,  4,  and  5 ;  and  for 
very  slow  currents  they  are  taken  to  be  nearly  as  2,  3,  and  4. 


WATEB-WAY.  387 

The  greatest  velocity  may  be  obtained  by  actual  measure- 
ment, by  means  of  floats,  current  metres,  or  other  suitable 
apparatus,  or  it  may  be  calculated  from  the  slope  of  the  bed 
or  the  river  at  and  near  this  locality. 

Having  determined  the  greatest  velocity,  the  mean  velocity 
is  taken  as  four-fifths  of  it.  Col.  Medley,  in  his  Treatise  on 
Civil  Engineering,  takes  the  mean  velocity  as  nine-tenths 
(nearly)  of  the  surface  velocity  when  the  latter  exceeds  three 
feet  per  second,  and  four-fifths  when  less  than  this. 

Having  determined  the  mean  velocity  of  the  natural  water- 
way, that  of  the  contracted  water-way  may  be  obtained  from 
the  following  expression, 

o 
v  =  m—  V, (163) 

8 

in  which  8  and  v  represent,  respectively,  the  area  and  mean 
velocity  of  the  contracted  water-way;  S  and  V,  the  same 
data  of  the  natural  water-way ;  and  m  a  constant,  which,  as 
determined  from  various  experiments,  may  be  represented  by 
the  number  1,045. 

Giving  to  s  a  particular  value,  that  for  v  may  be  deduced, 
and  may  then  be  compared  with  the  velocity  allowable  at 
this  locality ;  or,  assuming  a  value  for  #,  the  value  of  s  may 
be  deduced,  and  will  be  the  area  of  the  contracted  water- 
way. The  safest  width,  or  area  of  water-way,  in  many  cases 
may  be  inconveniently  great ;  therefore,  some  risk  must  be 
run  by  confining  the  floods  to  more  contracted  limits.  To 
reduce  this  risk  as  much  as  possible  is  the  object  of  the 
engineer  in  seeking  this  information.  With  this  information, 
the  engineer  can  decide  upon  the  number  of  piers,  hence  the 
number  of  spans  of  the  bridge.  Knowing  the  nature  of  the 
bottom,  the  character  and  kind  of  piers  and  abutments  may 
be  selected. 

518.  Design  or  plan  of  bridge. — Before  the  engineer  can 
complete  the  design  of  the  bridge,  it  is  necessary  that  he 
should  know  what  service  it  has  to  perform  :  whether  it  is  to 
be  a  common  or  a  railroad  bridge ;  whether  a  single  or  double- 
track  one.  This  information  being  given,  and  the  knowledge 
acquired  of  the  site  and  water-way  being  furnished  him,  he  is 
able  to  decide  whether  the  structure  shall  be  a  truss,  arched, 
or  suspension  bridge ;  and,  knowing  the  facilities  at  the  place 
for  the  construction  of  the  work,  can  prepare  an  estimate  of 
its  probable  cost. 

In  deciding  on  the  form  of  bridge  which  shall  best  com- 
bine efficiency  with  economy,  there  are  many  things  to  be 


388  CIVIL   ENGINEERING. 

considered.  The  cost  of  the  superstructure,  or  all  above  the 
piers  and  abutments,  increases  rapidly  with  the  length  of 
span.  Hence,  economy  would,  as  far  as  the  superstructure  is 
concerned,  demand  short  spans.  But  short  spans  require  an 
increase  in  the  number  of  piers.  When  the  height  is  small, 
the  stream  not  navigable,-  and  the  piers  easy  to  build,  short 
spans  may  be  used  ;  but,  if  the  foundations  are  in  bad  soils, 
if  the  river  is  deep,  with  a  rapid  current,  or  liable  to  great 
freshets,  if  it  is  navigable  and  requires  an  unobstructed 
water-way,  the  construction  of  piers  will  be  very  expensive, 
and  therefore  it  is  often  desirable  in  these  cases  that  there 
should  be  few  or  no  piers  in  the  stream  ;  hence,  long  spans 
are  necessary,  even  at  great  cost.  Good  judgment  and  accu- 
rate knowledge  on  the  part  of  the  engineer  will  be  necessary, 
in  order  that  these  and  similar  questions  should  be  decided 
correctly. 

EEECTION   OF   BRIDGE. 

519.  The  bridge  having  been  planned,  its  parts  all  prepared 
and  taken  to  the  site,  the  abutments  and  piers  built,  the  next 
step  is  to  put  it  in  position. 

There  are  three  methods,  which  have  already  been  named, 
viz.,  building  the  bridge  on  a  scaffolding  in  the  position  it  is 
to  occupy ;  building  it  and  rolling  it  in  position,  known  as 
launching  /  and  building  away  from  the  site  and  then  float- 
ing it  to  the  spot,  and  lifting  it  in  place. 

520.  Scaffolding. — The  scaffolding  is,  so  far  as  principle 
is  concerned,  the  same  as  that  already  described  under  the 
head  of   masonry.      That  used  for  bridge   construction  is 
simply  a  rough  but  rigid  trestling,  resting  on  the  ground,  or 
on   piles   when  the  scaffolding  is  over  water.     The  whole 
arrangement   is  sometimes   called   staging,  and  frequently 
false-works. 

By  means  of  this  scaffolding  the  different  pieces  of  the 
structure  are  lifted  in  place  and  fastened  together.  When 
the  bridge  is  finished  the  staging  is  removed.  This  method 
is  the  one  most  generally  used. 

521.  Launching. — This  method  has  been  used  where  the 
scaffolding  would  have  been  too  great  an  obstruction  to  the 
stream  or  too  costly.      Deep  and   rapid  rivers  or  ravines, 
where  the  bridge  is  erected  at  a  very  high  level,  or  rivers 
with   rapid   currents   subject  to  great    freshets,   are    cases 
where  scaffolding  would  be  costly,  and  in  some  cases  imprac- 
ticable. 


COST   OF  BRIDGE. 

522.  Floating  to    site    and   lifting   in  place.  —  This 
method  has  been  used  in  connection  with  the  last  method. 

In  this  method  the  truss  or  tube  is  placed  on  boats  01 
pontons,  and  floated  to  the  spot  it  is  to  occupy.  Then,  bj 
cranes  or  other  suitable  lifting  machinery,  the  truss  is  lifted 
to  its  place.  This  was  the  method  adopted  for  the  Britannia 
Tubular  Bridge. 

In  tidal  waters  this  method  has  been  used  with  great 
success.  The  truss  was  put  together  on  platforms  on  the 
decks  of  barges,  at  a  sufficient  height  above  the  surface  of 
the  water,  so  that  at  high  tide  the  truss  would  be  above  the 
level  of  its  final  position.  The  barges  were  then  floated  into 
position  at  high  tide,  and  as  the  tide  fell  the  truss  was  de- 
posited in  its  proper  place. 

523.  Cost. — The  cost  of  erecting  a  bridge  is  divided  gene- 
rally into  four  parts :   1,  Scaffolding ;  2,  Plant ;  3,  Labor ; 
4,  Superintendence. 

Scaffolding  — The  cost  of  this  forms  an  essential  part  of 
the  estimate,  and  depends  greatly  upon  the  facilities  for 
obtaining  the  proper  materials  in  the  vicinity  of  the  site. 

Plant. — This  is  a  technical  word  used  to  include  the  tools 
and  machinery  employed  in  the  work.  The  employment  of 
steam  in  so  many  ways  at  the  present  time  renders  this  item 
an  important  one  in  estimating  the  cost. 

Labor. — The  number  of  men,  their  wages,  subsistence,  and 
oftentimes  their  transportation,  have  all  to  be  considered 
under  this  head. 

Superintendence. — Good  foremen  and  able  assistants  are 
essential  to  a  successful  completion  of  the  work.  Their  wages 
may  be  included  in  the  last  item.  It  is  usual  to  allow  a  given 
percentage  on  the  estimate  to  include  the  cost  of  superintend- 
ence. 

Summing  these  four  items  together,  the  cost  of  erecting 
the  superstructure  of  the  bridge  may  be  estimated. 


PART   VII 

ROOFS. 


CHAPTER  XX. 

524.  The  term  roof  is  used   to  designate  the  covering 
placed  over  a  structure  to  protect  the  lower  parts  of  the 
Duilding  and  its  contents  from  the  injurious  effects  of  the 
weather.     It  consists  of  two  distinct  parts — the  covering  and 
the  frames  which  support  the  covering.     By  some  the  term 
roof  is  applied   only  to   the  "covering,"   exclusive  of  the 
frames. 

525.  jRoofs  are  of  various  forms — angular,  curved,  and 
flat,  or  nearly  so. 

The  most  common  form  of  roof  is  the  angular.  These 
vary  greatly  in  appearance  and  in  construction.  Some  of  the 
most  common  examples  of  the  angular  roof  are  the  ordinary 
gabled,  the  hipped,  the  curb  or  Mansard,  the  French  roof, 
etc. 

Curved  roofs  and  domes  are  frequently  used.  They  cost 
more  than  the  angular  roofs,  if  the  cost  of  the  abutments  be 
included.  But  if  the  abutments  already  exist  or  if  for  other 
reasons  they  have  to  be  built,  the  curved  roof,  under  these 
circumstances,  in  many  cases,  may  be  found  cheaper  and  more 
suitable. 

Flat  roofs  are  very  common,  especially  in  hot  climates. 
The  covering  of  these  roofs  rests  upon  beams  placed  in  a 
horizontal  position,  or  one  that  is  nearly  so.  The  slope  given 
them  is  generally  about  4°  with  the  horizontal. 

These  roofs  are  easy  to  construct,  and  are  simple  in  plan, 
but  they  are  heavy,  do  not  allow  the  water  to  escape  freely, 
and  there  is  a  waste  of  material  in  their  use. 

526.  Coverings. — The   coverings   of  roofs   are   made   of 
boards,  shingles,  slates,  mastics,  the  metals,  or  any  suitable 


ROOFS.  391 

material  which  will  stand  exposure  to  the  weather  and  afford 
a  water-tight  covering.  The  style  of  the  building,  and  the 
especial  object  to  be  attained,  will  govern  their  selection. 
The  extent  of  surface  covered  by  them  is  usually  expressed 
in  square  feet.  Sometimes  the  term  square  is  only  used,  in 
which  case  it  means  an  area  of  100  square  feet. 

The  weight  of  the  materials  used  for  the  covering  is  about 
as  follows : 

Material.  Weight  per  square  foot. 

Copper 1  Ib. 

Lead Tibs. 

Zincv 1.5  Ibs. 

Tin fib. 

Iron  (common) 3  Ibs. 

Iron  (corrugated) 3.5  Ibs. 

Slates 5  to  12  Ibs. 

Tiles 7  to  18  Ibs. 

Boards,  1  inch  thick 2£  Ibs. 

Shingles..  lib. 


- 


These  are  fastened  directly  upon  the  frames,  or  upon 
pieces  of  scantling  and  boarding  which  rest  on  the  frames. 

527.  Frames. — The  frames  which  support   the   covering 
have  their  exterior  shape  to  correspond  to  the  form  of  the 
roof.     These  frames,  known  generally  as  roof-trusses,  are 
tied   together  and  stiffened  by  braces  which   may  occupy 
either  a  horizontal  or  inclined  position,  and  may  be  either 
notched  upon  or  simply  bolted  to  the  trusses. 

The  trusses  are  placed  from  five  to  ten  feet  apart,  depend- 
ing upon  the  weight  of  the  covering  and  the  amount  of  load 
which  each  truss  has  to  support.  They  rest  usually  upon 
pieces  of  timber  called  wall-plates,  laid  on  the  wall  to 
distribute  the  pressure  transmitted  by  the  truss  over  a  larger 
surface  of  the  wall. 

528.  Although  nearly  the  last  part  of  a  building  which  is 
constructed,  the  roof  is  one  of  the  first  to  be  considered  in 
planning  the  building,  since  the  thickness  and  the  kind  of 
wall   depend  greatly   upon  the   weight  of  the  roof.     The 
weight  of  the  roof  and  the  size  of  the  "pieces  to  be  used  in  its 
construction,  when  the  roof  is  flat,  are  easily  determined. 
The  pieces  are  simple  beams,  subjected  only  to  cross-strains, 
and  the  joints  are  of  the  simplest  kind. 

When  the  roof  is  curved  or  inclined,  these  determinations 
are  more  difficult.  In  these  roofs  the  strains  on  the  parts 
produced  by  the  covering  are  of  different  kinds,  and  must  be 


392  CIVIL   ENGINEERING. 

determined  completely,  both  in  amount  and  kind,  before  the 
dimensions  of  the  different  pieces  can  be  fixed,  and  the  best 
form  of  joints  and  fastenings  selected. 

In  calculating  the  strains  on  a  roof-truss,  we>must  take 
.into  consideration,  besides  the  weight  of  the  covering  and  of 
the  truss  itself,  the  weight  of  the  snow,  ice,  or  water  which 
may  at  times  rest  upon  the  covering,  the  effect  due  the  action 
of  the  wind,  and  such  extra  loads  as  the  weight  of  a  ceiling, 
of  machinery,  of  floors,  etc.,  which  may  be  supported  by  the 
frames. 

The  weight  of  the  covering  varies,  as  has  been  shown, 
from  one  pound  to  twenty  pounds  upon  the  square  foot. 
The  weight  of  the  truss  increases  with  the  span,  but  it  is 
only  in  very  wide  spans  that  the  weight  of  the  parts  and  of 
the  whole  truss  have  to  be  considered. 

The  weight  of  snow  is  assumed  to  be  about  one-tenth  that 
of  the  same  bulk  of  water.  Knowing  the  maximum  depth 
of  the  falls  of  snow,  an  approximate  weight  may  be  deter- 
mined. Six  pounds  per  square  foot  is  the  estimated  weight 
of  snow  adopted  by  European  engineers.  A  greater  weight, 
even  as  high  as  twenty  pounds,  is  recommended  for  the 
northern  part  of  the  United  States. 

The  action  of  the  wind  is  very  great  in  some  localities. 
Tredgold  recommends  an  allowance  of  forty  pounds  to  the 
square  foot  as  an  allowance  for  its  effect. 

529.  Rise  and  span. — These  are  quantities  dependent 
upon  circumstances.  The  rise  is  dependent  upon  the  kind  of 
roof,  the  order  of  architecture  used  for  the  building,  and  the 
climate.  The  span  is  dependent  upon  the  size  of  the 
building. 

In  gabled  roofs  and  ordinarily  angled  roofs,  the  inclina- 
tion which  the  sides  of  the  roof  make  with  the  horizontal  is 
called  the  pitch.  In  countries  where  heavy  falls  of  snow 
are  common  the  pitch  is  ordinarily  made  quite  steep — al- 
though builders  are  now  more  generally  inclined  to  a  mode- 
rate pitch,  even  for  these  cases.  The  objections  to  a  steep 
pitch  are  the  exposing  of  a  greater  surface  of  the  roof  to  the 
direct  force  of  the  wind,  the  waste  of  room,  etc.  The  mate- 
rial of  which  the  covering  is  composed  affects  the  pitch.  An 
ordinary  roof  covered  with  shingles  should  have  a  pitch  of  at 
least  22-|  degrees ;  one  covered  with  slate  or  tiles  a  pitch 
something  greater,  between  23  and  30  degrees. 

The  style  of  roof  and  architecture  affect  the  pitch.  Gothic 
styles  and  parts  of  French  roofs  require  a  pitch  of  4:5  degrees, 
and  even  of  60  degrees. 


ROOFS. 


393 


530.  Materials  used  in  construction. — Wood  and  iron 
are  the  materials  used  for  the  construction  of  the  frames. 
The  truss  may,  as  in  other  frames,  be  made  entirely  of  wood, 
or  entirely  of  iron,  or  of  a  combination  of  the  two  materials. 


Wooden  Roof-trusses. 

531.  The  simplest  wooden  truss  is  the  triangular  frame. 
The  inclined  pieces  are  called  rafters  and  the  horizontal  one 
is  termed  the  tie-beam. 

It  is  used  for  spans  of  12  to  18  feet,  and  when  the  roof 
is  light.  For  spans  of  18  to  30  feet  the  king-post  truss 
(Fig.  205)  is  used.  Its  component  parts  are : 


FIG.  205. 


1.  The  principal  rafters. — These  are  the  inclined  pieces, 
B  B,  which  abut  against  each  other  or  against  the  king-post 
at  the  top. 

2.  The  tie-beam. — This  is  the  horizontal  beam,  A,  con- 
nected with  the  lower  ends  of  the  rafters  to  prevent  their 
spreading  out  under  the  action  of  the  load  placed  on  them. 

3.  The  king-post. — The  upright,  C,  framed  at  the  upper 
end  upon  the  rafters  and  connected  at  the  lower  end  with  the 
tie-beam. 

4.  Purlins. — These  are  horizontal  pieces,  E,  E,  notched  upon 
or  bolted  to  the  rafters  to  hold  the  frames  together  and  to 
form  supports  for  the  common  rafters,  F,  F. 

5.  Common  rafters. — These  are  inclined  pieces,  F,  F,  of 
smaller  dimensions  than  the  principal  rafters,  placed  from  1 
to  2  feet  apart  and  intended  to  support  the  covering. 

6.  Struts. — The  inclined  pieces,   D,  D,   framed  into   the 
principal  rafters  and  king-post  to  prevent  the  rafters  from 
sagging  at  the  middle. 


394 


CIVIL   ENGINEERING. 


If  the  king-post  and  struts  be  removed,  the  simple  triangu- 
lar truss  is  left. 

532.  Queen-post  truss, — This  truss  is  employed  for  spans 
from  30  to  45  feet  long.  Its  parts  (Fig.  206)  are  all  shown  in 
the  figure  ;  C,  C,  being  the  queen-posts. 


FIG.  206. 


533.  Iron  roof- trusses, — Wooden  roof -trusses  have  been 
used  for  wider  spans  than  those  named,  but  the  use  of  iron  in 
building  has  enabled  the  engineer  to  construct  roof-trusses  of 
wider  spans  which  are  much  lighter  and  present  a  better 
appearance. 

These  trusses  are  sometimes  made  of  wood  and  iron  in 
combination,  as  we  have  seen  in  bridge-trusses,  but  now  they 
are  more  generally  made  entirely  of  iron. 

The  coverings  are  frequently  made  of  iron,  mostly  corru- 
gated, and  are  fastened  to  the  purlins  by  the  usual  methods 
for  iron -work. 


DETERMINATION    OF   THE   KIND  AND  AMOUNT   OF   STRAINS    ON  THE 
PARTS    OF    A   ROOF-TRUSS. 

534.  Amount  and  kind  of  strains  upon  the  different 
parts  of  the  simple  king-post  truss. — The  method  of 
determining  the  amount  and  kind  of  strains  on  the  simple 
triangular  frame  has  already  been  explained.  (Art.  256.) 
It  is  usual,  except  in  very  short  spans  and  where  the  tie-beam 
supports  nothing  but  its  weight,  to  support  the  middle  point 
of  this  piece  by  a  king-post.  To  find  the  strains  on  a  tri- 
angular frame  with  a  king-post,  let  A  B  and  A  C  (Fig.  207) 
be  the  rafters,  B  C,  the  tie-beam,  and  A  H,  the  king-post.  The 
king-post  is  so  framed  on  the  rafters  at  A,  as  to  hold  up  any 
load  which  it  has  to  support.  It  is  connected  with  the  tie- 
beam  in  such  a  manner  as  to  keep  the  middle  point,  H,  in  the 
same  straight  line  with  B  and  C. 


ROOFS. 


395 


The  strains  on  this  truss  are  produced  most  usually  by  a 
uniform  load  on  the  rafters  and  a  load  on  the  tie-beam. 
Denote  by  I,  the  length  of  either  rafter ;  by  w,  the  load  on 
Linit  of  length,  including  the  weight  of  the  rafters ;  by  W', 


a  unit 


FIG.  207. 

the  weight  of  the  tie-beam,  including  the  load  it  has  to  sup 
port,  as  a  ceiling,  floor,  etc.,  and  by  a,  the  angle  ABC. 

The  load  on  one  of  the  rafters,  as  A  B,  will  be  wl,  and  acts 
through  the  middle  point,  or  at  a  distance  from  B  equal  to  \l. 
The  strains  produced  by  this  load  are  compressive  on  the 
rafter  and  tensile  on  the  tie-beam,  and  the  amount  for  each 
may  be  determined,  as  shown  in  Art.  254. 

The  king-post  is  used  to  prevent  the  sagging  of  the  tie- 
beam  at  its  middle  point,  it  therefore  supports,  besides  its 
own  weight,  -fW  (Art.  186),  which  produces  a  strain  of  ten- 
sion on  the  king-post  and  which  is  transmitted  by  it  to  A, 
where  it  acts  as  a  load  suspended  from  the  vertex  of  the 
frame.  The  strains  produced  by  it  on  the  rafters  and  tie- 
beam  may  be  determined  as  in  Ait.  256. 

The  strains  being  known  in  amount  and  kind  for  each  piece, 
can  now  be  summed  and  the  total  amount  on  the  different 
parts  determined. 


535. — Strains  on  a  king-post  truss  framed  with  struts. 
— Let  Fig.  208  represent  an  outline  of  this  truss.  Let  D  F  and 
F  G  be  the  struts  framed  in  the  king-post  and  supporting  the 
rafters  at  their  middle  points. 

The  truss  is  supposed  to  be  strained  by  a  load  uniformly 
distributed  over  the  rafters. 


396  CIVIL   ENGINEERING. 

• 

Adopt  the  notation  used  in  the  previous  case  and  repre- 
sent by  ft,  the  angle  A  D  F.  We  may  neglect  without 
material  error  the  weight  of  the  struts  and  king-post,  their 
weights  being  small  compared  with  the  load  on  the  rafters. 

The  load  acts  vertically  downwards  and  is  equal  to  wl  for 
each  rafter.  Acting  obliquely,  it  tends  to  compress  and  bend 
them.  Each  rafter  is  a  case  of  a  beam  resting  on  three  points 
of  support,  hence  the  pressure  on  either  strut  is  due  to  the 
action  of  ^wl. 

Pressure  on  the  struts. — The  pressure  on  the  strut  D  F 
arises  from  the  action  of  the  component  of  %wl  perpendicu- 
lar to  the  rafter  at  the  point,  D.  Denote  by  Pj  the  pressure 
on  the  strut  in  the  direction  of  its  axis.  To  keep  the  point,  D, 
in  the  same  straight  line  with  A  and  B,  the  resistance  offered 
by  the  strut  must  be  equal  to  the  force  acting  to  deflect  the 
rafter  at  that  point.  Hence  there  results, 

P!  sin  ft  =  %wl  cos  a.     ...    (164) 

From  which  we  find 

cos  a 

— — -r-, 
sin  /3' 

for  the  pressure  on  the  strut,  D  F.  In  the  same  way  the  pres- 
sure on  the  strut  F  G  is  obtained,  which  in  this  case  is  exactly- 
equal  in  amount. 

Tension  on  king-post. — This  pressure,  P1?  is  transmitted 
through  the  strut  to  the  king-post  at  F.  Resolving  this  force 
into  its  components  respectively  perpendicular  and  parallel 
to  the  axis  of  the  king-post,  we  find  the  component  in  the 
direction  of  the  axis  to  be  Pt  sin  (ft  —  a). 

The  king-post  supports  the  tie-beam  at  its  middle  point. 
Represent  as  before  by  W,  the  weight  of  the  tie-beam  and 
its  load,  and  we  have  -|W  for  the  pull  on  the  king-post  from 
this  source.  Represent  the  total  stress  of  tension  by  Tl5  and 
there  results, 

T!  =  2PX  sin  (ft  -  a)  +  f  W.     .     .     (165) 

Substituting  in  this  for  Pj,  its  value  just  found,  and  the 
value  of  Tt  will  be  known. 

Tension  on  the  tie-beam. — Denote  by  T  the  tension  on 
the  tie-beam  produced  by  the  thrust  along  the  rafters,  and 
by  Q,  the  vertical  reaction  at  B  caused  by  the  load  on  the 
rafters. 

The  relation  between  the  normal  components  to  the  rafter, 


BOOFS.  397 

at  B,  of  the  three  forces,  Q,  T,  and  -fowl  acting  at  that  point, 
may  be  expressed  by  this  equation, 

T  sin  a  =  Q  cos  a  —  -fowl  cos  a.     .     (166) 

From  which  the  value  of  T  can  be  obtained  when  Q  is 
known. 

Since  the  truss  is  symmetrical  with  respect  to  a  vertical 
through  A,  the  sum  of  the  reactions  at  B  and  C,  due  to  the 
strains  on  the  rafters,  is  2Q,  and  is  equal  to  the  total  load 
placed  on  the  rafters,  which  is  2wl  4-  -jj-W'.  Hence 


2Q  =  2wZ  +  f  W, 
and 

Q  =  wl  + 


which,  substituting  in  equation  (166),  gives, 

T  sin  a  =  \%wl  cos  a  +  A^'  cos  a> 
and 


Strains  on  the  rafters.  —  The  forces  acting  in  the  direc- 
tion of  the  rafters  produce  compressive  strains,  and  those 
perpendicular,  transverse  strains.  These  are  determined  as 
previously  shown. 

Size  of  the  pieces.  —  Having  found  all  the  strains,  the 
limit  on  the  unit  of  cross-section  may  be  assumed  and  the 
dimensions  of  the  pieces  obtained. 

Remark.  —  It  is  well  to  notice,  that  if  we  substitute  for 
P!,  its  value  in  the  expression  for  T1}  the  tension  on  the  king- 
post, that  we  will  get 


which  may  be  put  under  the  form 


It  is  seen  from  this  value  of  T15  that  whenever  yS  is  equal 
to  90°  or  differs  but  slightly  from  it,  the  expression  will 
reduce  to  the  form 


T!  =  f  (W'  +  tool  cos2  a). 
536.  Strains  on  the  queen-post  truss.  —  It  is  easily  seen 


398 


CIVIL  ENGINEERING. 


from  the  foregoing  how  the  strains  on  this  truss  may  be  de- 
termined. It  is  usual  to  suppose  the  truss  (Fig.  209)  separ- 
ated into  two  parts ;  one  the  primary  truss,  BAG,  and  the 
other,  the  secondary  trapezoidal  truss,  B  D  G  C. 


FIG.  209. 


In  some  cases,  short  rafters  from  C  to  G,  and  B  to  D,  are 
placed  in  contact  with  the  principal  rafters,  A  C  and  A  B, 
which  further  strengthens  the  truss  by  the  additional  thickness 
given  to  the  rafters  in  this  part  of  the  truss,  and  more  fully 
satisfies  the  condition  of  a  secondary  trapezoidal  truss  placed 
within  a  triangular  frame  to  increase  its  strength.  There 
are  various  other  modifications  of  this  truss,  but  the  method 
of  determining  the  strains  is  not  affected  by  them. 

Iron  Roof-trusses. 

537.  The  trussing  already  explained  under  the  head  of 
Bridges  enters  largely  into  iron  roof-trusses.  One  of  the 
most  common  forms  is  the  one  in  which  the  rafters  are 
trussed. 


FIG.  210. 

Roof-truss  with  trussed  rafters. — A  common  method 
of  supporting  the  middle  point  of  a  rafter  is  shown  in  Fig. 
210.  In  this  case  the  lower  end  of  the  strut,  instead  of 
abutting  against  a  king-post,  is  held  up  by  tie-rods  joining  it 
with  the  ends  of  the  rafters. 


BOOF8. 

It  is  seen  from  the  figure  that  each  rafter,  with  the  strut 
and  tie-rod,  forms  a  simple  king-post  truss  inverted.  The 
tie-rod  connecting  the  points,  E  and  F,  completes  the  truss. 
This  tie-rod  sustains  the  horizontal  thrust  produced  by  the 
strains  on  the  rafters,  preventing  its  action  on  the  walls  at  the 
points  of  support,  B  and  C. 

In  this  truss  the  rafters  are  equal  in  length,  and  make 
equal  angles  with  the  horizon  ;  the  struts  are  placed  at  the 
middle  points  and  perpendicular  to  the  rafter  ;  and  the 
strains  are  produced  by  a  uniform  load  resting  on  the 
rafters. 

Use  the  notation  of  the  previous  cases,  and  denote  by  a 
the  angle  ABC;  by  £,  the  angle  D  B  E  ;  by  25,  B  C  ;  by  d, 
the  height  A  H  ;  and  by  d',  the  distance  A  K.  The  truss  is 
symmetrical  with  respect  to  a  vertical  A  H,  through  the  vertex, 
A.  Suppose  the  truss  cut  in  two  along  this  line,  A  H,  we  may 
preserve  the  equilibrium,  upon  removing  the  left  half,  by 
substituting  two  horizontal  forces,  one  at  A  and  the  other  at  K. 
Suppose  this  done,  and  represent  these  by  H  and  T  respec- 
tively. As  the  weight  of  the  tie-rods  and  struts  is  small 
compared  with  the  load  on  the  rafters,  we  may  neglect  it  with- 
out material  error. 

The  reaction  at  B  is  equal  to  wl. 

The  external  forces  acting  on  the  right  half  of  the  frame  are 
the  reaction  at  B,  the  horizontal  forces  H  and  T  at  A  and  K, 
and  the  load  on  the  rafter  including  its  own  weight.  These 
forces  act  in  the  same  vertical  plane. 

The  analytical  conditions  for  equilibrium  are 

H  —  T  =  0,     and     wl-wl  =  0, 
and  the  bending  moment  at  B  is 


We  find  the  value  of  H  =  }  . 

d 

The  external  forces  are  now  all  known  and  the  strains  pro- 
duced by  them  may  be  determined. 

Pressure  on  the  struts.  —  Considering  the  rafter  as  a 
single  beam,  there  results 

P!  =  f  wl  cos  a, 

for  the  pressure  on  either  strut. 

Tension  on  the  tie-rods  of  the  rafters.  —  Let  Tt  be  the 
tension  on  the  tie-rod  B  E,  and  Ta  the  tension  on  A  E. 


4:00  CIVIL  ENGINEERING. 

At  the  point,  B,  the  normal  pressure  must  be  equal  to  the 
normal  component  of  the  resultant  of  the  forces,  wl  and  Ta 
acting  at  that  point,  which  may  be  expressed  as  follows  : 


cos  a  =  wl  cos  a  —  Tt  sin  /?, 
and  at  A,  for  the  same  reason,  we  have 

•ffWl  cos  a  =  H  sin  a  —  T2  sin  /3. 
These  equations  give,  since  H  is  known, 


(169) 


for  the  tensions  on  the  tie-rods  B  E  and  A  E. 

Tension  on  the  main  tie-rod,  EF,   of  the  truss. — 

From  the  analytical  condition, 

H  —  T  =  0, 

there  results, 

T  =  H  =  i-^A   .    .    .    (170) 

This  may  be  verified.  The  stresses,  Pl5  Tb  and  T2,  in  the 
pieces  connected  at  E  (Fig.  210)  have  been  determined. 
These  forces  with  T  must  be  in  equilibrium  at  E.  Let  us 
find  the  components  of  these  forces  in  the  direction  of  the 
strut,  D  E,  and  a  perpendicular  to  the  strut  at  E.  (Fig.  211.) 

For  equilibrium,  we  have  the  fol- 
£  lowing : 

\\  D  (Tt  +  T2)  sin  ft  -  T  sin  a  -  Pt  =  0, 

\  /  and 

r  ^ ^/ 

XVv  (T2  —  TI)  cos  &  +  T  cos  a  =  0. 


/ 

\  T}       Substituting  in   the   first    of   these 
pf  x    equations,  the  values  of  Pt,  T1?  and  T2, 

FIG  211.  already  obtained,  there  results, 

-J-J-  wl  cos  a  -f-  H  sin  a  —  f  wl  cos  a  —  T  sin  a  —  0,  or  H  =  T. 

In  a  similar  manner,  by  substitution  in  the  2d,  it  can  be 
shown  that  the  condition  is  satisfied,  or  H  =  T. 

Compression  on  the  rafters.— The  compression  on  the 
rafter  at  B  is  due  to  the  components  of  the  forces  acting  at 
that  point  parallel  to  the  rafter.  Hence 

Compression  at  B  =  wl  sin  a  +  TI  cos  /3, 


BOOFS. 


401 


and 


Compression  at  A  =  H  cos  a  +  T2  cos  0.       (171) 

Frequently  in  the  construction  of  this  truss,  the  struts  are 
extended  until  they  meet  the  tie-rod  -joining  B  and  C.  (Fie. 
212.) 


PIG.  212. 

In  this  case  the  stresses  are  the  same  as  those  just  deter- 
mined in  the  struts  and  rafters,  but  are  less  in  the*  secondary 
tie-rods,  because  of  the  increase  in  the  angle  ft. 

538.  When  the  span  is  considerable,  this  method  of  truss- 
ing is  oftentimes  used  to  increase  the  number  of  supports  for 
the  rafter.  By  adding  to  the  trussed  rafter,  the  two  struts, 
bf&nd  cd  (Fig.  213),  and  the  two  secondary  tie-rods,  fD  and 
#  D,  two  additional  points  of  support  are  furnished  to  the 
rafter. 


FIG.  213. 

The  points,  b  and  <?,  are  midway  between  B  D  and  A  D,  divid 
ing  the  rafter  into  four  equal  parts,  and  making  the  triangles 
Bj  D  and  D  d  k  equal  to  each  other  and  similar  to  B  E  A. 

Using  the  previous  notation,  the  reaction  at  B  is  wl,  and  the 

horizontal  force  at  A  is  -J -™ — ,  as  in  previous  case.     The 

Cu 
external  forces  are  all  known. 

Pressure  on  the  struts.— The  struts  are  respectively  per- 
pendicular to  the  rafter;  the  normal  components  of  the 
forces  acting  at  5,  D,  and  c  will  give  the  amount  of  pressure 
on  each  strut,  due  to  the  load  acting  at  these  points.  Repre- 
sent this  component  at  D  by  P1?  at  b  and  c  by  Pa,  and  at  A 
26 


4-02  CIVIL  ENGINEERING. 

and  B  by  P8.  Since  the  rafter  is  kept  by  the  struts  in  such  ft 
position  that  b,  D,  and  c  are  in  the  same  straight  line  with  A 
and  B,  it  is  an  example  of  a  beam  resting  on  five  supports,  and 
we  have, 

P3  =  -^Yzwl  cos  a,  P2  =  f  wl  cos  a,  and  Pt  =  $%wl  cos  a. 


This  value  of  P2  is  the  amount  of  pressure  acting  on  either 
of  the  struts,  bfor  cd,  and  the  strain  on  them  is  determined. 
That  on  D  E  is  still  to  be  determined. 

Tension  on  the  secondary  tie-rods.  —  Let  T!  be  the  ten- 
sion on  the  rod,  Bf,  and  we  have, 


wl  cos  a  =  wl  cos  a  —  T!  sin 
from  which  we  get 


And  in  the  same  way  we  find  the  tension  T\  on  kd  to  be 

Hsina  cos  a 

1  i  = 


.  -rrs*    •       f 

sm  ft  sin  ft 

Denote  by  T2,  T8,  T'2,  and  T'8  the  tensions  on/D,/E,  d  D, 
and  d  E  respectively.  Since  an  equilibrium  exists  between 
the  forces  acting  at  the  point  f,  and  the  same  at  d,  the  com- 
ponents of  these  forces,  taken  respectively  parallel  and  per- 
pendicular to  the  rafter,  must  fulfil  the  following  conditions  : 

T2  +  T8-  Tt  =  0,  and  (T8  -  T2  -  Tt)  sin/3  +  P2  =  0,at/, 

and 

T'j  +  T'8  -  T'i  =  0,  and  (T'8  -  T',  -  T'J  sin  ft  +  P2  =  0,  at  d. 

The  values  of  Tl9  P2,  and  T^,  have  already  been  found. 
The  values  for  the  others  are  easily  deduced.  They  will  be 
as  follows  : 


and  T's  =  -r—  (H  sin  a  -  f&wl  cos  a). 


The  strains  of  tension  and  compression  on  all  the  secondary 
pieces  have  been  obtained  excepting  for  the  strut,  D  E,  at  the 
middle.  This  can  now  be  determined. 


KOOFS.  403 

Strain  on  strut,  D  E,  at  the  middle. — This  strain  is  due 
to  the  pressure,  Ply  and  the  components  of  T2  and  T'2  in  the 
direction  of  the  strut,  or 

Compression  on  D  E  =  P  =  Pt  +  (T2  +  T'2)  sin  £. 

Substituting  in  this  for  T2,  T2,  and  P1?  their  values  already 
found,  we  finally  obtain, 

P  =  $%wl  cos  a, 

for  the  stress  in  the  strut,  D  E. 

The  amount  and  kind  of  strain  on  each  piece  are  now 
known,  and  the  strength  of  the  truss  may  therefore  be  deter- 
mined. 

539.  Roof -truss  in  which  the  rafters  are  divided  into 
three  segments  and  supported  at  the  points  of  division  J>y 
struts  abutting  against  king  or  queen-posts. 

This  form  of  truss  shown  in  Fig.  214  is  in  common  use  for 
roofs.  In  this  case,  the  rafters  are  trisected  respectively  at 
the  points,  H,  D,  G,  and  M,  by  the  struts  H  K,  D  F,  G  F,  and 


L        F        K 
FIG.  214. 

M  L,  which  have  their  lower  ends  connected  with  and  abutting 
against  the  vertical  rods  at  the  points  K,  F,  and  L,  where  these 
rods  are  fastened  to  the  tie-rod  B  C. 

The  usual  method  of  determining  the  amount  of  strains  on 
the  different  parts  of  a  frame  of  this  kind  is  to  consider  it  as 
formed  of  several  triangular  ones.  In  this  particular  case, 
we  consider  the  truss  A  B  C  as  made  up  of  the  secondary 
trusses,  B  H  K,  B  D  F,  and  B  F  A,  on  the  right  of  A  F,  and 
a  similar  set  on  the  left  of  it. 

The  strains  are  supposed  to  arise  from  a  uniform  load  over 
the  rafters,  the  weight  of  the  vertical  ties  and  the  struts  being 
neglected,  as  in  the  previous  cases. 

In  the  previous  examples,  the  rafters  have  been  regarded 
as  single  beams  resting  on  two,  three,  five,  etc.,  points  of  sup- 
port, and  the  reactions  of  these  points  of  support  have  been 
taken  as  the  value  of  the  load  resting  upon  them.  This  pro- 
cess may  be  followed  in  this  case  and  is  to  be  preferred, 
whenever  the  rafters,  A  B  and  A  G,  are  continuous. 


404:  CIVIL   ENGINEERING. 

In  most  treatises  on  roofs,  the  action  of  the  load  on  the 
points  of  support  is  considered  in  a  different  manner.  There 
are  two  general  methods.  Taking  either  half  of  a  truss 
of  the  kind  just  described,  one  method  supposes  that  each 
segment  of  the  rafter  supports  one-third  of  the  entire  load 
on  the  rafter ;  or,  each  segment  is  considered  a  beam  sup- 
ported at  its  ends  and  uniformly  loaded.  According  to  this 
hypothesis,  since  %wl  is  the  load  on  the  segment,  ^wl  will 
act  at  the  points,  H  and  D,  and  ±wl,  at  B  and  A,  of  the  half 
ABF. 

The  other  method  assumes  the  pressures  exerted  at  the 
four  points  of  support  to  be  equal  to  each  other,  that  is,  %wl 
to  be  the  load  acting  at  each  of  the  points,  B,  H,  D,  and  A. 
This  is  sometimes  called  "  the  method  of  equal  distribution 
of  the  load." 

Adopting  the  first  method,  assuming  one-third  of  the  load 
on  the  rafter  as  resting  on  each  segment,  let  us  first  determine 
the  strains  in  the  secondary  truss,  B  H  K. 

Strains  on  B  HK. — By  hypothesis,  the  pressure  at  H  is  \wl, 
acting  vertically  downwards.  The  problem  then  is  the  case 
of  a  simple  triangular  frame  sustaining  a  load  at  the  vertex. 

Denote  by  a,  the  angle  H  B  K  ;  since  the  triangle  is  isos- 
celes, the  components  of  %wl  along  the  rafter  and  strut  are 

each  equal  to  4-^ ,  and   develop   compressive    stresses  in 

sin  a 

H  B  and  H  K. 

The  stress  transmitted  to  B  produces  a  vertical  pressure  on 
the  point  of  support  equal  to  \wl  and  a  stress  of  tension  in 
B  K  equal  to  \wl  cot  a. 

In  like  mariner,  the  stress  transmitted  to  K  produces  a  ver- 
tical pull  at  that  point  equal  to  \wl  which  is  sustained  by  the 
tie-rod,  D  K,  and  a  horizontal  stress  equal  to  and  directly  op- 
posed to  the  stress  of  tension  at  B. 

Strains  on  B  D  F, — The  problem  in  this  case  is  that  of  the 
simple  triangular  frame,  sustaining  a  weight  at  the  vertex. 

The  load v  acting  at  D  is  %wl,  increased  by  the  pull  on  the 
tie-rod,  D  K,  or  \wl,  and  is  supported  by  the  rafter  B  D  and 
the  strut  D  F.  Since  these  pieces  do  not  make  equal  angles 
with  the  vertical  through  D,  the  components  of  %wl  in  the 
directions  of  these  pieces  are  not  equal.  Kesolving,  we 

wl  , 

find  the  one  in  the  direction  of  the  rafter  will  be  -5-7-— ,  and 

bill    CL 

the  other  along  the  strut,  i^— 5- ;  £  being  the  angle  D  F  K. 


KOOF8.  405 

The  first  of  these  is  transmitted  to  B,  where  it  produces  a 
vertical  pressure  equal  to  {wl,  and  a  tensile  stress  in  the 
tie-beam  equal  to  {wl  cot  a. 

The  other,  transmitted  to  F,  produces  a  pull  on  the  king- 
post equal  to  \wl,  and  a  tensile  stress  in  the  tie-beam  equal 
to  and  directly  opposed  to  that  at  B  produced  by  the  com- 
ponent acting  along  the  rafter. 

Strains  on  BFA.  —  The  stress  in  AD  is  due  to  the  assumed 
load,  {wl  at  A  and  the  transmitted  stress  in  the  king-post, 
{wl,  or  is  equal  to  \wl. 

Resolving  this  into  its  components  along  the  rafter  A  B 

and  a  horizontal  at  A,  we  have  for  the  first.  {  -^  —  ,  and 

•  sin  a' 

for  the  latter,  {  wl  cot  a. 

The  former  transmitted  to  B  produces  a  vertical  pressure 
equal  to  {wl,  and  a  tensile  stress  in  the  tie-beam  equal  to  {wl 
cot  a. 

The  horizontal  component  at  A  is  balanced  by  an  equal  and 
directly  opposite  component  due  to  the  half  A  C  F. 

Strains  on  the  whole  truss.  —  Knowing  the  strains  on 
one-half,  and  the  truss  being  symmetrical  about  the  vertical 
through  A,  the  stresses  in  all  the  pieces  can  now  be  determined. 
Summing  and  recapitulating,  the  stresses  are  as  follows  : 

T     D  u     /~  M     1  w%       1   wl       .   wl       .wl 
In  B  H—  C  M=4—  :  --  1-4—  :  --  \-{-  —  =f-s  -  ,  compressive. 
sin  a      sin  a      sin  a      sin  a 


-. 

sin  a     2sm  a     dsm  a 


«    DA=GA=*4^-, 
sm  a 


H   K=M  L=J-,  andDF=G  F= 

6  sin  «  sin 


"    D   K=G  L  =  {wl,  and  A  F  =  \wl  +  {wl  =  \wl,  tensile, 
"    B  K=C  L  =  $wl  cot  or,  and  K  F  =  F  L  =  \wl  cot  a,     " 

By  the  use  of  moments.  —  These  same  values  may  be  ob- 
tained by  using  the  "  method  of  sections."  To  apply  this 
method  to  determine  the  stresses  in  the  rafter,  suppose 
a  vertical  section  of  the  rafter  made  on  the  right  of  and  con- 
secutive to  A,  and  take  the  point  F  as  the  centre  of  moments. 
Represent  the  compressive  stress  in  the  segment,  A  D,  of 


406  CIVIL   ENGINEERING. 

the  rafter  cut  by  this  section,  by  C^  Its  direction  is  paral. 
lei  to  A  B,  and  its  lever  arm,  which  denote  byj?,  will  be 
equal  to  a  perpendicular  let  fall  from  F  upon  the  rafter. 
The  reaction  at  B  and  the  load  on  the  rafter  are  known. 
For  equilibrium  we  would  have, 

B  F 
d  x  p  =  wl  x  B  F  —  wl  x  -g-, 

whence 

d  =  \wl  x  —  . 

We  find  p  to  be  equal  to  -j-  ,  which  being  substituted  in 
this  expression  gives 


Substituting  in  (172)  the  value  of  d  =  I  sin  a,  we  obtain 

wl 


vrhich  is  the  same  value  already  determined. 

If  the  same  method  be  applied  to  the  segment  H  B,  we 

will  find  the  value  of  C3  to  be  equal  to  4-  -^  —  . 

6  sin  a 

540.  In  the  preceding  roof  -truss,  the  inclined  pieces  were 
struts  and  the  verticals  were  ties.  Another  form  of  truss  is 
one  in  which  the  verticals  are  struts  and  the  diagonals  are 
ties.  (Fig.  215.)  The  rafters  are  subdivided  into  a  number 
of  equal  segments.  At  each  point  of  division,  a  strut  is 
placed,  and  kept  in  a  vertical  position  by  the  main  tie-beam 
and  the  inclined  tie-rods,  as  shown  in  the  figure. 


FIG.  215. 


The  methods  previously  explained  will  enable  the  student 
to  determine  the  kind  and  amount  of  strains  on  each  piece  of 
the  truss. 


BOOF8. 


407 


541.  It  has  been  recommended  to  check  the  accuracy  of 
the  calculations  by  some  other  method  than  the  one  used ; 
the  graphical  method  is  a  very  convenient  one  for  this  purpose. 
Let  us  apply  this  method  to  finding  the  strains  in  the  roof- 
truss  referred  to  in  Art.  539. 

The  load  over  the  rafters  is  supposed  to  act  as  there  taken, 
viz.,  -J-  at  A  and  B,  and  %  at  H  and  D,  each. 

Assume  any  point,  as  0.  From  0,  on  a  vertical  line,  lay 
off,  according  to  a  scale,  Ob  =  %wl,  bh  =  $wl,  hd  =  fyol, 
and  da  =  \wl.  These  distances  represent  the  loads  acting 
at  B,  H,  D,  and  A,  respectively.  Their  sum  00  =  wl,  hence, 


aO=—wl  represents  the  reaction  at  B,  due  to  the  load  acting 
on  the  half  A  B  F  of  the  truss.  The  forces  at  B  are  Ob,  aO, 
and  the  stresses  in  the  pieces  B  H  and  B  K.  Through  5, 
draw  bf  parallel  to  B  H,  and  through  a,  draw  af  parallel  to 
B  K.  The  polygon  aObfa  will  represent  the  system  of  forces 
acting  at  B,  and  the  lines  fa  and  bfwill  represent  the  inten- 
sities of  the  stresses  in  K  B  and  B  H,  respectively,  at  B,  and 
may  be  taken  off  with  the  same  scale  used  to  lay  off  the  ver- 
tical forces,  Ob,  bh,  etc. 

It  is  seen  that  the  forces  acting  at  H  are  the  weight  \wl  = 
bh,  the  stress  £>/,  and  the  unknown  stresses  in  H  K  and  H  D. 
Through  /*,  draw  fa  parallel  to  H  K,  and  through  A,  draw  hg 
parallel  to  H  D.  The  polygon,  fbhqf  will  represent  the  in- 
tensities of  the  forces  acting  at  H. 

The  forces  acting  to  strain  B  K  and  H  K  have  been  deter- 
mined ;  the  forces  acting  at  K  in  the  directions  of  K  D  and 
K  F  are  unknown.  Through  g,  draw  gk  parallel  to  K  D,  and 
through  a,  draw  ak  parallel  to  K  F,  forming  the  polygon 
qfgka  ;  the  lines  gk  and  ka,  will  represent  the  intensities  of 
the  stresses  in  D  K  and  K  F. 

The  stresses  in  the  pieces  K  D  and  HD  being  known,  the 
stresses  in  DA  and  DF  can  be  determined. 


408 


CIVIL  ENGINEERING. 


In  a^  similar  way,  the  stresses  in  the  other  pieces  can  be 
determined. 

542.  Application  of  graphical  method  to  the  roof 
•with  trussed  rafters.— Let  us  apply  the  same  method  tc 
the  trussed  roof  of  Art.  537.  Instead  of  the  frame  being  uni- 
formly loaded  over  the  rafters,  consider  it  as  supporting  a 
load  W  at  the  vertex  A.  (Fig.  217.) 

The  applied  forces  acting  on  the  frame  are  the  load  "W 
and  the  reactions  at  B  and  C.  Assume  a  point,  as  0,  and  lay 
off  on  a  vertical  line  the  distance  Ob  to  represent  W.  The 
distances  be  and  cO  will  represent  the  reactions  at  B  and  at 
C.  Through  5,  draw  ~bd  parallel  to  B  D,  and  through  <?,  the 
line  cd  parallel  to  B  E.  The  triangle  bed  will  represent  the 


FIG.  217. 

system  of  forces  acting  at  B.  Through  0,  draw  the  line 
Og  parallel  to  AC,  and  through  0,  draw  the  line  eg  parallel  to 
C  F.  The  triangle  Oeg  will  represent  the  forces  acting  at  C. 

Going  to  E,  since  the  load  on  the  truss  has  been  supposed 
to  act  at  A,  there  will  be  no  strain  on  D  E,-  and  the  forces  at 
E  will  be  those  acting  in  the  direction  B  E  already  found,  and 
the  unknown  forces  along  E  A  and  E  F.  Through  d,  draw  da 
parallel  to  E  A,  and  through  0,  draw  ca  parallel  to  E  F.  The 
triangle  cda  will  represent  these  three  forces  acting  at  E. 
And  in  the  same  way,  the  triangle  ega  would  represent  the 
strains  on  the  pieces  at  F. 

If  there  had  been  a  force  acting  at  E  in  the  direction  of 
D  E,  then  there  would  have  been  three  unknown  forces  acting 
at  E,  and  we  could  not  have  solved  the  problem  until  one  of 
these  were  known. 


KOOFS.  409 


Purlins. 

543.  The  pnrlins  are  simply  beams,  and  are  considered  as 
resting  on  two  or  more  supports,  according  to  the  number 
of  frames  connected  by  them.  The  strains  are  easily  deter 
mined. 


CONSTRUCTION    OF    EOOFS. 

544.  The  most  important  element  of  the  roof  is  the  frame. 
The  same  rules  given  for  frames,  and  the  general  methods 
described  for  their  construction  apply  to  the  construction  of 
the  roof-truss. 


410  CTVTL   ENGINEERING. 


PART   VIII. 

KOADS,  RAILROADS,  AND   CANALS. 


CHAPTER  XXI. 

ROADS. 

545.  A  road  is  an  open  way  or  passage  for  travel,  forming 
a  communication  between  two  places  some  distance  apart. 

A  path  or  track  over  which  a  person  can  travel  on  foot  is 
the  simplest  form  of  a  road.  A  line,  having  been  marked 
out  or  "  blazed"  between  two  places,  is  soon  beaten  into  a  well- 
defined  path  by  constant  use.  A  person  travelling  over  a  road 
like  this  will  tind  nothing  but  a  beaten  path  on  the  surface  of 
the  ground,  with  few  or  no  modifications  of  its  surface,  and 
generally  with  no  conveniences  for  crossing  the  streams  or 
rivers  which  intersect  it. 

As  the  travel  over  a  road  of  this  kind  increases  and  beasts 
of  burden  begin  to  be  used  for  packing  the  merchandise, 
baggage,  etc.,  which  are  to  be  carried  over  the  route,  modifi- 
cations and  improvements  of  the  path  become  necessary. 
For  convenient  passage  of  the  animals,  the  path  must  be 
widened,  the  brush  and  undergrowth  removed,  temporary 
bridges  constructed  or  means  of  ferriage  provided  for  cross- 
ing streams  of  any  considerable  depth,  and  steep  ascents  and 
descents  must  be  modified  and  rendered  practicable  for  the 
pack-animals.  The  term  "trail"  is  used  to  designate  the 
original  path  and  also  the  path  when  improved  so  that  it  can 
be  used  by  pack-animals. 

Since  transportation  by  wheels  is  cheaper  and  more  rapid 
than  by  pack-animals,  the  next  step  will  be  to  still  further 
improve  the  road  so  that  vehicles  on  wheels  can  be  used  over 
the  route.  This  necessitates  a  still  further  widening  of  the 
trail,  a  further  reduction  of  the  slopes  so  as  to  render  them 
practicable  for  carts  and  wagons,  the  providing  of  means  to 


ROADS.  411 

cross  the  streams  where  they  cannot  be  forded,  and  the  raising 
of  the  ground  in  those  localities  where  it  is  liable  to  be  over 
flowed.  In  this  condition,  the  trail  is  called  a  road. 

As  the  travel  over  this  kind  of  road  increases,  the  wants  and 
conveniences  of  the  community  demand  a  further  improve- 
ment of  the  road  so  that  the  time  taken  in  going  over  it  and 
the  cost  of  transportation  shall  be  reduced.  This  is  effected 
by  shortening  the  road  where  possible,  by  reducing  still  further 
the  ascents  and  descents  or  by  avoiding  them,  and  by  improv- 
ing the  surface  of  the  road. 

It  has  been  proved  that  a  horse  can  draw  up  a  slope  of  ^ 
only  one-half  the  load  he  can  draw  on  a  level.  Hence,  a  level 
road  would  enable  one  horse  to  do  the  work  required  of  two 
on  a  road  with  these  slopes. 

It  has  been  shown  that  a  horse  can  draw  over  a  smooth, 
hard  road,  as  one  of  broken  stone,  from  three  to  four  times 
as  much  as  he  can  draw  on  a  soft  earthen  road.  It  therefore 
follows  that  an  improvement  of  the  surface  will  be  accom 
panied  by  a  reduction  both  in  time  and  cost  of  the  transpor- 
tation. 

546.  The  engineer  may  be  required  to  lay  out  and  make 
a  road  practicable  for  wagons  connecting  two  settlements 
or  points,  in  a  wild,  uninhabited,  and  therefore  unmapped 
country,  as  is  the  case  frequently  on  our  frontier,  or  he  may 
be  required  to  plan  and  construct  a  road  having  for  its  ob- 
jects the  reduction  of  time  and  expense  of  transportation, 
in  a  country  of  which  he  has  maps  and  other  authentic 
information.  In  either  case,  the  general  principles  guiding 
the  engineer  are  the  same.  These  may  be  considered  under 
the  following  heads :  1st,  Direction  •  2d,  Gradients  j  3d, 
Cross-Section ;  4th,  Road-Coverings  •  5th,  Location ;  6th, 
Construction. 


DIRECTION. 

547.  Other  things  being  equal,  the  shortest  line  between 
the  two  points  is  to  be  adopted,  since  it  costs  less  to  con- 
struct ;  costs  less  for  repairs ;  and  requires  less  time  and  labor 
to  travel  over  it. 

But  straightness  will  be  found  of  less  consequence  than 
easy  ascents  and  descents,  and  as  a  rule  must  be  sacrificed  to 
obtain  a  level  or  to  make  a  road  less  steep. 

Good  roads  wind  around  hills  instead  of  running  over 
them,  and  this  they  may  often  be  made  to  do  without  increasing 
their  lengths.  But  even  if  the  curved  road,  which  is  prac- 


4:12  CIVIL   ENGINEERING. 

tically  level,  should  be  longer,  it  is  the  better ;  for  on  it  a 
horse  will  draw  a  full  load  at  his  usual  rate  of  speed,  while 
on  the  road  over  the  hill,  the  load  must  be  diminished  or  the 
horse  must  reduce  his  rate  of  speed. 

Roads  often  deviate  from  the  straight  line  for  reasons 
of  economy  in  construction,  such  as  to  avoid  swampy,  marshy, 
or  bad  ground,  or  to  avoid  large  excavations,  or  to  reach 
points  on  streams  better  suited  for  the  approaches  of  bridges, 
etc. 

Great  care  must  be  exercised  in  deciding  on  the  line  which 
the  road  is  to  follow.  If  the  line  is  badly  chosen,  the  ex- 
pense of  construction  and  repair  may  be  so  great  that  it  may 
finally  be  necessary  to  change  the  line  and  adopt  a  new  one. 

548.  The  considerations    which  should  govern  the   selec- 
tion of   the  line  are :  to  connect  the  termini  by  the  most 
direct   and  shortest  line  ;  to  avoid  unnecessary   ascents  and 
descents  ;  to  select  the  position  of  the  road  so  that  its  longi- 
tudinal slopes  shall  be  kept  within  given  limits ;  and  to  so 
locate  the  line  that  the  cost  of  the  embankments,  excavations, 
bridges,  etc.,  shall  be  a  minimum. 

The  wants  of  the  community  in  the  neighborhood  of  the 
line  oftentimes  affect  the  direction  of  the  line,  since  it  may 
be  advisable  and  even  more  economical  in  the  end  to  change 
the  direction  so  as  to  pass  through  important  points  which  do 
not  lie  on  the  general  direction  of  the  road  than  to  leave 
them  off  the  road. 

GRADIENTS. 

549.  Theoretically,  every  road  should  be  level.     If  they 
are  not,  a  large  amount  of  the  horse's  strength  is  expended  in 
raising  the  load  he  draws  up  the  ascent.     Experiment  has 
shown  that  a  horse  can  draw  up  an  ascent  of  y-J-g-,  only  90 
per  cent,  of  the  maximum  load  he  can  draw  on  a  level ;  up 
an  ascent  of  ^,  he  can  draw  about  80  per  cent. ;  of  -g^,  he 
can  draw  only  64  per  cent. ;  of  ^,  only  50  per  cent. ;  and  of 
•jijf,  only  25  per  cent. 

These  numbers  are  affected  by  the  nature  and  condition  of 
the  road,  being  different  for  a  rough  and  for  a  smooth  road, 
the  resistance  of  gravity  being  more  severely  felt  on  the 
latter. 

A  level  road  is  therefore  the  most  desirable,  but  can  seldom 
be  obtained.  The  question  is  to  select  the  maximum  slope 
or  steepest  ascent  allowable. 

An  ascent  affects  chiefly  the  draught  of  heavy  loads,  as  has 
been  already  shown. 


GBADIENTS.  413 

A  descent  chiefly  affects  the  safety  of  rapid  travelling. 

550.  The  slope  or  grade  of  a  road  depends  upon  the  kind 
of  vehicle  used,  the  character  of  the  road-covering,  and  the 
condition  in  which  the  road  is  kept.     From  the  experiments 
above  mentioned  it  would  seem  that  the  maximum  grade  for 
ascent  should  not  be  greater  than  1  in  30,  although  1  in  20 
may  be  used  for  short  distances. 

For  descent,  the  grade  should  be  less  than  the  angle  of 
repose,  or  that  inclination  at  which  a  vehicle  at  rest  would 
not  be  set  in  motion  by  the  force  of  gravity.  This  angle 
varies  with  the  hardness  and  smoothness  of  the  road-covering, 
and  is  affected  by  the  amount  of  friction  of  the  axles  and 
wheels  of  the  vehicles.  On  the  best  broken  stone  roads  iii 
good  order,  for  ordinary  vehicles,  the  maximum  grade  is 
taken  at  1  in  35. 

Steeper  grades  than  these  named  produce  a  waste  of  ani- 
mal power  in  ascending  and  create  a  certain  amount  of  dan- 
ger in  descending. 

551.  Although  theoretically  the  road  should  be  level,  in 
practice  it  is  not  desirable  that  it  should  be  so,  on  account  of 
the  difficulty  arising  of  keeping  the  surface  free  from  water. 
A  moderate  inclination  is  therefore  to  be  selected  as  a  mini- 
mum slope  for  the  surface  of  the  road.     This  slope  is  taken 
at  1  in  125,  and  in  a  level  country  it  is  recommended  to  form 
the  road  by  artificial  means  into  gentle  undulations  approxi- 
mating to  this  minimum. 

It  is  generally  thought  that  a  gently  undulating  road  is 
less  fatiguing  to  a  horse  than  one  which  is  level.  Writers 
who  hold  this  opinion  attempted  to  explain  it  physiologically, 
stating  that  as  one  set  of  muscles  of  the  horse  is  brought  into 
play  during  the  ascent  and  another  during  the  descent,  that 
some  of  the  muscles  are  allowed  to  rest,  while  others,  those  in 
motion,  are  at  work.  This  explanation  has  no  foundation  in 
fact,  and  is  therefore  to  be  rejected.  The  principal  advan- 
tage of  an  undulating  road  is  not  the  rest  it  gives  the  horse, 
but  the  facilities  which  are  afforded  to  the  flowing  of  the 
water  from  the  surface  of  the  road. 


CROSS-SECTION. 

552.  The  proper  width  and  form  of  roadway  depend  upon 
the  amount  and  importance  of  the  travel  over  the  road. 

Width. — The  least  width  enabling  two  vehicles  to  pass 
with  ease  is  assumed  at  16£  feet.  The  width  in  most  of  the 
States  is  fixed  by  law. 


4:14  CIVIL   ENGINEERING. 

In  England,  the  width  of  turnpike  roads  approaching 
large  towns,  on  which  there  is  a  great  amount  of  travel,  is 
60  feet.  Ordinary  turnpike  roads  are  made  35  feet  wide.  Or- 
dinary carriage  roads  across  the  country  are  given  a  width 
of  25  feet ;  for  horse-roads,  the  width  is  8  feet ;  and  for  foot- 
paths, 6-J  feet. 

Telford's  Holyhead  road  is  made  32  feet  wide  on  level 
ground  ;  28  feet  wide  in  moderate  excavations  ;  and  22  feet 
in  deep  excavations  and  along  precipices. 

In  France  there  are  four  classes  of  main  roads.  The  first 
or  most  important  are  made  66  feet  wide,  the  middle  third  of 
which  is  paved  or  made  of  broken  stone.  The  second  class 
are  52  feet  wide  ;  the  third  are  33  feet  wide  ;  and  the  fourth 
are  26  feet  wide.  All  these  have  the  middle  portion  ballasted 
with  broken  stone. 

The  Roman  military  roads  had  their  width  established  by 
law,  at  twelve  feet  when  straight  and  sixteen  when  crooked. 

Where  a  road  ascends  a  hill  by  zigzags  it  should  be  made 
wider  on  the  curves  connecting  the  straight  portions  ;  this  in- 
crease of  width  being  one-fourth  when  the  angle  included 
between  the  straight  portions  is  between  120°  and  90°,  and 
one-half  when  the  angle  is  between  90°  and  60°. 

553.  Form  of  roadway. — The  surface  of  the  road  must 
not  be  flat,  but  must  be  higher  at  the  middle  than  at  the 
sides,  to  allow  the  surface  water  to  run  off  freely. 

If  the  surface  is  made  flat,  it  soon  becomes  concave  from 
the  wear  of  the  travel  over  it,  and  forms  a  receptacle  for 
water,  making  a  puddle  if  on  level  ground,  and  a  gulley  if 
the  ground  is  inclined. 

The  usual  shape  given  the  cross-section  of  the  roadway 
is  that  of  a  convex  curve,  approaching  in  form  a  segment  of 
a  circle  or  an  ellipse.  This  form  is  considered  objectionable 
for  the  reasons  that  water  stands  on  the  middle  of  the  road  ; 
washes  away  its  sides ;  that  the  road  wears  unequally,  and 
is  very  apt  to  wear  in  holes  and  ruts  in  the  middle  ;  and  that 
when  vehicles  are  obliged  to  cross  the  road,  they  have  to 
ascend  a  considerable  slope. 

554.  The  best  form  of  the  upper  surface  of  the  roadway  is 
that  of  two  inclined  planes  rounded  off  at  their  intersection 
by  a  curved  surface.     The  section  of  this  curved  surface  is  a 
flat  segment  of  a  circle  about  flve  feet  in  length. 

The  inclination  of  the  planes  will  be  greatest  where  the 
surface  of  the  road  is  rough  and  least  where  it  is  smoothest 
and  hardest.  A  slope  of  -fa  is  given  a  road  with  a  broken 
stone  covering,  and  may  be  as  slight  as  -^  for  a  road  paved 
with  square  blocks.  The  transverse  slope  should  always 


DITCHES.  415 

exceed  the  longitudinal  slope  of  the  road,  so  as  to  prevent  the 
surface  water  from  running  too  far  in  the  direction  of  the 
length  of  the  road. 

On  a  steep  hillside,  the  surface  of  the  roadway  should  be 
a  plane  inclined  inwards  to  the  face  of  the  hill.  A  ditch  on 
the  side  of  the  road  next  to  the  hill  receives  the  surface 
water. 

555.  Foot-paths. — On  each  side  of  the  roadway,  foot-paths 
should  be  made  for  the  convenience  of  passengers  on  foot. 
They  should  be  from  five  to  six  feet  wide  and  be  raised  about 
six  inches  above  the  roadway.  The  upper  surface  should 
have  an  inclination  towards  the  "  side  channels,"  to  allow  the 
water  to  flow  into  them  and  thence  into  the  ditches.  When 
the  natural  soil  is  firm  and  sandy,  or  gravelly,  its  surface  will 
serve  for  the  foot-paths ;  but  if  of  loam  or  clay,  it  should  be 
removed  to  a  depth  of  six  inches  and  the  excavation  filled 
with  gravel. 

Sods,  eight  inches  wide  and  six  inches  thick,  should  be 
laid  against  the  side  slope  of  the  foot-path  next  to  the  road,  to 
prevent  the  wash  from  the  water  running  in  the  side  chan- 
nels. 

Fences,  hedges,  etc.,  where  the  road  is  to  be  enclosed, 
should  be  placed  on  the  outside  of  the  foot-paths,  and  outside 
of  these  should  be  the  ditches.  (Fig.  218.) 


FIG.  218. — a,  cross-section  of  roadway;  ft,  ft,  foot-paths  ;  /,/,  fences; 
c?,  d,  ditches ;  s,  s,  side  drains. 

556.  Ditches. — Ditches  form  an  important  element  in  the 
construction  of  a  good  road. 

The  surface  of  the  road  has  been  given  a  form  by  means 
of  which  the  water  falling  on  it  is  carried  off  into  the  gut- 
ters or  side  channels  of  the  road,  whence  it  is  conveyed  by 
side  drains,  s,  s  (Fig.  218),  into  ditches,  which  immediately 
carry  off  all  the  water  which  enter  them. 

The  ditches  are  sunk  to  a  depth  of  about  three  feet  below 
the  roadway,  so  that  they  shall  thoroughly  drain  off  the 
water  which  may  pass  through  the  surface  of  the  roadway. 
These  ditches  should  lead  to  the  natural  water- courses  of  the 
country,  and  have  a  slope  corresponding  to  the  minimum  lon- 
gitudinal slope  of  the  road.  Their  size  will  depend  upon 
circumstances,  being  greater  where  they  are  required  to  carry 


416  CIVIL   ENGINEERING. 

away  the  water  from  side-hills  or  where  they  are  made  in 
wet  grounds.  A  width  of  one  foot  at  the  bottom  will  gen- 
erally be  sufficient. 

There  should  be  a  ditch  on  each  side  of  the  road,  on  level 
ground  or  in  cuttings.  One  is  sufficient  where  the  road  is  on 
the  side  of  a  hill. 

557.  Side-slopes. — The    side-slopes  of  the   cuttings  and 
embankments  on  each  side  of  the  road  vary  with  the  nature 
of  the  soil. 

Rock  cuttings  may  be  left  vertical  or  nearly  so,  Common 
earth  should  have  a  slope  of  at  least  f,  and  sand,  -J.  Clay  is 
treacherous  and  requires  different  slopes  according  to  its  liabil- 
ity to  slip  and  the  presence  of  water.  The  slope  required  in 
each  case  is  best  determined  by  observing  the  slope  assumed 
by  these  earths  in  the  locality  of  the  work  where  exposed  to 
the  weather. 

When  the  road  is  in  a  deep  cutting,  the  side  slopes  should 
not  be  steeper  than  J,  so  as  to  allow  the  road,  by  its  exposure 
to  the  sun  and  wind,  to  be  kept  dry. 

Whenever  the  side-slopes  are  of  made  earth,  earth  removed 
and  placed  in  position  like  that  of  an  enbankment,  the  slopes 
should  be  more  gentle. 

ROAD-COVERINGS. 

558.  The  road-covering  of  a  common  country  road,  and 
most  generally  of  all  the  new  roads  in  our  country,  is  the 
natural  soil  thrown  on  the  road  from  the  ditches  on  each  side, 
in  many  cases  there  are  even  no  ditches,  and  the  road-cover- 
ing or  upper  surface  of  the  roadway  is  the  natural  soil  as  it 
exists  on  the  hard  subsoil  beneath,  when  the  soft  material  has 
been  removed  by  scraping  or  by  some  other  method. 

Roads  of  this  kind  are  deficient  in  the  qualities  of  hardness 
and  smoothness.  To  improve  these  roads,  it  is  necessary  to 
cover  the  surface  with  some  material,  as  wood,  stone,  etc., 
which  will  substitute  a  hard  and  smooth  surface  for  the  soft 
and  uneven  earth,  and  which,  acting  as  a  covering,  will  pro- 
tect the  ground  beneath  from  the  action  of  the  water  that 
may  fall  upon  it. 

559.  Roads  may  be   classified    from  their  coverings  as 
follows : 

I.  EARTH  ROADS. 

II.  ROADS  OF  WOOD. 

III.  GRAVEL  ROADS. 

IV.  ROADS  OF  BROKEN  STONK. 


COBDTJBOY  EOADS.  417 

Y.  ROADS  PAVED  WITH  STONE. 

VI.  KOADS   COVERED   OE   PAVED   WITH   OTHEB  MATF.RTAT.fl. 

VII.  TRAM-EOADS. 


L   EAETH  EOADS. 

560.  These  are  the  most  common  and  almost  the  only  kind 
of  roads  in  this  country.  From  what  has  been  said,  we  know 
that  they  are  deficient  in  hardness  and  generally  in  smooth- 
ness. In  wet  weather,  when  there  is  much  travel  of  a  heavy 
kind  over  them,  they  become  almost  impassable. 

The  principal  means  of  improvement  for  these  roads  are  to 
reduce  the  grades,  thoroughly  drain  the  roadway,  and  freely 
expose  the  roadway  to  the  influence  of  the  sun  and  wind.  In 
repairing  them,  the  earth  used  to  fill  the  holes  and  hollows 
should  be  as  gravelly  as  possible  and  free  from  muck  or 
mould.  Stones  of  considerable  size  should  not  be  used,  as 
they  are  liable  to  produce  lumps  and  ridges,  making  an  un- 
even surface  disagreeable  to  travel  upon. 


H.   EOADS   OF  WOOD. 

561.  Corduroy  roads. — When  a  road  passes  over  a  marsh 
or  soft  swampy  piece  of  ground  which  cannot  be  drained,  or 
the  expense  of  which  would  be  too  great,  a  corduroy  road 
is  frequently  used.     This  kind  of  road  is  made  by  laying 
straight  logs  of  timber,  either  round  or  split,  cut  to  suitable 
lengths,  side  by  side  across  the  road  at  right  angles  to  its 
length. 

It  is  hardly  worthy  of  the  name  of  a  road,  and  is  extremely 
unpleasant  to  persons  riding  over  it,  but  it  is  nevertheless 
extremely  valuable,  as  otherwise,  the  swamp  across  which  it 
is  laid  would  at  times  be  impassable. 

562.  Plank  roads. — In  districts  where  lumber  is  cheap  and 
gravel  and  stone  cannot  be  easily  obtained,  road-coverings  of 
plank  have  been  used. 

The  method  most  generally  adopted  in  constructing  a  road 
of  this  class  consists  in  laying  a  flooring  or  track,  eight  feet 
wide,  of  boards  from  nine  to  twelve  inches  in  width  and  three 
inches  in  thickness.  The  boards  rest  upon  two  parallel  rows 
of  sleepers,  or  sills,  laid  lengthwise  of  the  road,  and  having 
their  centre  lines  about  four  feet  apart,  or  two  feet  from  the 
axis  of  the  road. 

The  boards  are  laid  perpendicular  to  the  axis  of  the  road, 
27 


4:18  CIVIL  ENGINEERING. 

experience  having  shown  that  this  position  is  as  favorable  to 
their  durability  as  any  other  and  is  also  the  most  economical. 

When  the  road  is  new  and  well  made,  it  offers  all  the  ad- 
vantages of  a  good  road  and  is  a  very  pleasant  one  to  use. 
But  when  the  planks  become  worn  and  displaced  it  makes  a 
very  disagreeable  and  indifferent  road. 

Some  years  ago  they  were  much  used,  but  as  a  general 
thing  they  are  no  longer  built  except  under  very  peculiar 
and  urgent  circumstances. 

HI.    GRAVEL   ROADS. 

563.  These  are  roads  upon  which  a  covering  of  good  gravel 
has  been  laid. 

The  roadway  is  first  prepared  by  removing  the  upper  layer 
of  soft  and  loose  earth,  and  thoroughly  draining  the  road. 
The  bed  is  sometimes  of  the  shape  of  the  upper  surface  of  the 
road,  but  more  generally  it  is  merely  made  level :  on  this  a 
layer  of  gravel  about  four  inches  in  thickness  is  laid,  and 
when  compacted  by  the  travel  over  it  another  layer  is  laid, 
and  so  on  until  a  thickness  of  sixteen  inches  at  the  centre 
has  been  reached. 

It  is  advisable  to  compress  the  bed  by  rolling  it  well  with 
a  heavy  iron  roller  before  beginning  to  lay  the  gravel.  In 
some  cases  a  bed  of  broken  stone  has  been  u?ed. 

Gravel  from  the  river  shores  is  generally  too  clean  for  this 
kind  of  road,  there  not  being  enough  clayey  material  mixed 
with  it  to  bind  the  grains  together.  On  the  other  hand, 
gravel  from  pits  is  apt  to  be  too  dirty  and  requires  a  partial 
cleansing  to  fit  it  for  this  purpose. 

The  gravel  used  should  be  sifted  through  screens,  and  all 
pebbles  exceeding  two  inches  in  diameter  be  broken  into 
small  pieces  or  rejected. 

The  iron  roller  can  be  advantageously  used  to  assist  in 
compacting  the  layers  of  gravel  as  they  are  put  on  the  road. 

A  gravel  road  carefully  made,  with  good  side  ditches  to 
thoroughly  drain  the  road-bed,  forms  an  excellent  road. 

Some  gravel  roads  are  very  poor,  even  inferior  to  an  earth 
road,  caused  in  a  great  measure  by  using  dirty  gravel  which 
is  carelessly  thrown  on  the  road  in  spots,  which  cause  the  road 
1o  soon  wear  into  deep  ruts  and  hard  ridges. 

IV.    ROADS    OF   BROKEN    STONE. 

564.  The  covering  of    roads  of  this  class,  both   in  this 
country  and  Europe,  is  composed  of  stone  broken  into  small 


TELFOED   BOADS.  4:19 

angular  fragments.  These  fragments  are  placed  on  the  natu- 
ral bed  in  layers,  as  in  the  gravel  road,  or  they  may  be  placed 
in  layers  on  a  rough  pavement  of  irregular  blocks  of  stone. 

565.  Macadamized  roads. — When  the  stone  is  placed  on 
the  natural  road-bed,  the  roads  are  said  to  be  "  macadamized," 
a  name  derived  from  Mr.  Me  Adam,  who  iirst  brought  this 
kind  of  road  into  general  use  in  England. 

The  construction  of  this  road  is  very  similar  to  that  just 
given  for  a  gravel  road.  The  roadway  having  received  its 
proper  shape  and  having  been  thoroughly  drained,  is  covered 
with  a  layer  of  broken  stones  from  three  to  four  inches  thick. 
This  layer  is  then  thoroughly  compacted  by  allowing  the 
travel  to  go  over  it  and  by  rolling  it  also  with  heavy  iron 
rollers  ;  care  being  taken  to  fill  all  the  ruts,  hollows,  or  other 
inequalities  of  the  surface  as  fast  as  they  are  formed.  Suc- 
cessive layers  of  broken  stone  are  then  spread  over  the  road 
and  treated  in  the  same  manner,  until  a  thickness  of  between 
eight  and  twelve  inches  of  stone  is  obtained.  Care-is  taken 
that  the  layers,  when  they  are  spread  over  the  surface,  are 
not  too  thick,  as  it  will  be  difficult,  even  if  it  be  possible,  to 
get  the  stone  into  that  compact  condition  so  necessary  for  a 
good  road  of  this  kind. 

566.  Telford  roads. — This  is  the  name  given  to  the  broken 
stone  roads  in  which  the  stone  rests  on  a  rough  pavement 
prepared  for  the  bed.     (Fig.  219.) 


PIG.  219. 


This  pavement  is  formed  of  blocks  of  stone  of  an  irregular 
pyramidal  shape ;  the  base  of  each  block  being  not  more 
than  five  inches,  and  the  top  not  less  than  four  inches. 

The  blocks  are  set  by  the  hand  as  closely  in  contact  at  their 
bases  as  practicable ;  and  blocks  of  a  suitable  size  are  selected 
to  give  the  surface  of  the  pavement  a  slightly  convex  shape 
from  the  centre  outwards.  The  spaces  between  the  blocks 
are  filled  with  chippings  of  stone  compactly  set  with  a  small 
hammer. 

A  layer  of  broken  stone,  four  inches  thick,  is  then  laid 
over  this  pavement,  for  a  width  of  nine  feet  on  each  side  of 
the  centre ;  no  fragment  of  this  layer  should  measure  over 


4-20  CIVIL  ENGINEERING. 

two  and  a  half  inches  in  any  direction.  A  layer  of  broken 
Btone  of  smaller  dimensions,  or  of  clean  coarse  gravel,  is 
spread  over  the  wings  to  the  same  depth  as  the  centre  layer. 

The  road- covering,  thus  prepared,  is  thrown  open  to  travel 
until  the  upper  layer  has  become  perfectly  compact ;  care 
having  been  taken  to  fill  in  the  ruts  as  fast  as  formed  with 
fresh  stone,  in  order  to  obtain  a  uniform  surface.  A  second 
layer,  about  two  inches  in  depth,  is  then  laid  over  the  centre 
of  the  roadway ;  and  the  wings  receive  also  a  layer  of  new 
material  laid  on  to  a  sufficient  thickness  to  make  the  outside 
of  the  roadway  nine  inches  lower  than  the  centre.  A  coat- 
ing of  clean  coarse  gravel,  one  inch  and  a  half  thick,  is  then 
spread  over  the  surface,  and  the  road-covering  is  considered 
as  finished. 

The  stone  used  for  the  pavement  may  be  of  an  inferior 
quality  in  hardness  and  strength  to  the  broken  stone  on  top, 
as  it  is  but  little  exposed  to  the  wear  and  tear  occasioned  by 
travelling.  The  surface-stone  should  be  of  the  hardest  kind 
that  can  be  procured. 

567.  Kind  of  stone  used  for  broken  stone  roads. — The 
stone   used  for  these   roads  should  be  selected  from  those 
which  absorb  the  least  water,  and  are  also  hard  and  not  brit- 
tle.    All  the  hornblende  rocks,  porphyry,  compact  feldspar, 
and  some  of  the  conglomerates  furnish  good,  durable  road- 
coverings.     Granite,  gneiss,  limestone,  and   common    sand- 
stones are  inferior  in  this  respect,  and  are  used  only  when  the 
others  cannot  be  obtained. 

568.  Repairs. — Broken  stone  roads  to  be  good  must  be 
kept  in  thorough  repair.     If  the  road  is  kept  in  order  it  will 
need  no  repairs.     The  difference  between  "  kept  in  order  " 
and  "  repairs  "  is  that  the  latter  is  an  occasional  thing,  while 
the  former  is  a  daily  operation.     To  keep  the  road  in  order 
requires  that  the  mud  and  dust  be  daily  removed  from  the 
surface  of  the  road  and  that  all  ruts,  depressions,  etc.,  be  at 
once  filled  with  broken  stone. 

It  is  recommended  by  some  that  when  fresh  material  is 
added,  the  surface  on  which  it  is  spread  should  be  broken 
with  a  pick  to  the  depth  of  half  an  inch  to  an  inch,  and  the 
fresh  material  be  well  settled  by  ramming,  a  small  quantity 
of  clean  sand  being  added  to  make  the  stone  pack  better. 
When  not  daily  repaired  by  persons  whose  sole  business  it  is  to 
keep  the  road  in  good  order,  general  repairs  should  be  made 
in  the  spring  and  autumn  by  removing  all  accumulations  of 
mud,  cleaning  out  the  side  channels  and  other  drains,  and 
adding  fresh  material  where  requisite. 

If  practi  cable,  the  road -surf  ace  at  all  times  should  be  kept 


ROMAN   ROADS.  421 

free  from  an  accumulation  of  mud  and  dust,  and  the  surface 
preserved  in  a  uniform  state  of  evenness  by  the  daily  addition 
of  fresh  material  wherever  the  wear  is  sufficient  to  call  for  it. 
"Without  this  constant  supervision,  the  best  constructed  road 
will,  in  a  short  time,  be  unfit  for  travel,  and  with  it  the  weak- 
est may  at  all  times  be  kept  in  a  tolerably  fair  condition. 


V.  ROADS  PAVED  WITH  STONE. 

569.  A  good  pavement  should  offer  but  little  resistance  to 
the   wheels,  and  at  the  same  time  give  a  firm  foothold  to 
horses ;  it  should  be  durable,  free  from  noise  and  dirt,  and 
so  constructed  as  to  allow  of  its  easy  removal  and  replace- 
ment whenever  it  may  be  necessary  to  gain  access  to  gas  or 
water  pipes  which  may  be  beneath  it. 

570.  Roman  roads. — The   ancient   paved   Roman   roads, 
traces  of  which  may  still  be  seen  as  perfect  as  when  first 
made,  were  essentially  dressed  stone  pavements  with  concrete 
foundations  resting  on  sub-pavements.     The  entire  thickness 
of  the  road-covering  was  about  three  feet,  and  was  made  as 
follows : 

The  direction  of  the  road  was  marked  out  by  two  parallel 
furrows  in  the  ground,  and  the  loose  earth  from  the  space 
between  them  removed.  A  bed  of  mortar  was  then  spread 
over  the  earth,  and  on  this  the  foundation  (statumeii),  com- 
posed of  one  or  two  courses  of  large  flat  stones  in  mortar, 
was  laid.  On  this  foundation  was  placed  a  course  of  con- 
crete (rudm),  composed  of  broken  stones.  If  the  stones 
were  freshly  broken,  three  parts  of  stone  to  one  of  lime  were 
used  ;  if  the  stone  came  from  old  buildings,  two  parts  of  lime 
were  used.  On  this  course  a  third  (nucleus),  composed  of 
broken  bricks,  tiles,  pottery,  mixed  with  mortar,  was  placed. 
In  this  layer  was  imbedded  the  large  blocks  of  stone  (sum- 
ma  crustd)  forming  the  pavement.  These  stones  were  ir- 
regular in  form,  rough  on  their  under  side,  smooth  on  their 
upper,  and  laid  so  that  the  upper  surface  should  be  level. 
They  were  laid  with  great  care  and  so  fitted  to  each  other  as 
to  render  the  joints  almost  imperceptible. 

When  the  road  passed  over  marshy  ground,  the  foundation 
was  supported  by  timber- work,  generally  of  oak ;  the  timber 
was  covered  with  rushes,  reeds,  and  sometimes  straw,  to  pro- 
tect it  from  contact  with  the  mortar. 

On  each  side  of  the  roadway  were  paved  foot-paths. 

571.  English  paved  roads. — Some  of  the  paved  roads  in 
England  are  partial  imitations  of  the  Koman  road.  This 


422  CIVIL   ENGINEERING. 

pavement  (Fig.  220)  was  constructed  by  removing  the  sur- 
face of  the  soil  to  the  depth  of  a  foot  or  more  to  obtain  a  iirm 
bed.  If  the  soil  was  soft  it  was  dug  deeper  and  a  bed  of 
sand  or  gravel  made  in  the  excavation.  On  this  a  broken 
stone  road-covering  similar  to  those  already  described  was 
laid.  On  this  broken  stone  was  spread  a  layer  of  fine  clean 


FIG.  220. 

gravel,  two  and  a  half  inches  thick,  on  which  rested  the  pav- 
ing stones.  The  paving  stones  were  of  a  square  shape,  and 
were  of  different  sizes,  according  to  the  nature  of  the  travel 
over  the  road.  The  largest  size  were  ten  inches  thick,  nine 
inches  broad,  and  twelve  inches  long ;  the  smallest  were  six 
inches  thick,  five  inches  broad,  and  ten  inches  long.  Each 
block  was  carefully  settled  in  its  place  by  means  of  a  heavy 
rammer ;  it  was  then  removed  in  order  to  cover  the  side  of 
the  one  against  which  it  rested  with  hydraulic  mortar;  this 
being  done,  the  block  was  replaced,  and  properly  adjusted. 
The  blocks  of  the  different  courses  across  the  roadway  break 
joints. 

This  pavement  fulfils  all  the  conditions  required  of  a  good 
road -covering,  presenting  as  it  does  a  hard  even  surface  to 
the  action  of  the  wheels,  and  reposing  on  a  firm  bed  formed 
by  the  broken-stone  bottoming.  The  mortar-joints,  so  long 
as  they  remain  tight,  will  effectually  prevent  the  penetration 
of  water  beneath  the  pavement. 

572.  Belgian  pavement. — This  pavement,  so  named  from 
its  common  use  in  Belgium,  is  made  with  blocks  of  rough 
stone  of  a  cubical  form  measuring  between  eight  and  nine 
inches  along  the  edge  of  the  cube.  These  blocks  are  laid  on 
a  bed  of  sand ;  the  thickness  of  this  bed  is  only  a  few  inches 
when  the  soil  beneath  is  firm,  but  in  bad  soils  it  is  increased 
to  from  six  to  twelve  inches.  The  transversal  joints  are  usu- 
ally continuous,  and  those  in  the  direction  of  the  axis  of  the 
road  break  joints.  In  some  cases  the  Hocks  are  so  laid  that 
the  joints  make  an  angle  of  45°  with  the  -*ds  of  the  roadway, 
one  set  being  continuous,  the  other  set  breaking  joints.  By 
this  arrangement  of  the  joints,  the  wear  upon  the  edges  of 
the  blocks,  by  which  the  upper  surface  soon  assumes  a  con- 
vex shape,  is  diminished.  It  has  been  ascertained  by  experi- 
ence, that  when  the  blocks  are  laid  in  the  usual  manner,  the 


WOODEN   PAVEMENTS.  423 

wear  upon  the  edges  of  the  block  is  greatest  at  the  joints 
which  run  transversely  to  the  axis. 

When  a  bed  of  concrete  is  used,  instead  of  or  in  addition 
to  a  bed  of  sand,  and  the  upper  surface  of  the  blocks  is  rec- 
tangular instead  of  square,  there  results  a  pavement  much 
used  in  New  York  City. 

573.  Cobble-stone  pavement. — Rounded  pebbles  (cobble 
stones)  are  used  frequently  for  pavements.     This  pavement 
is  composed  of  round  or  egg-shape  pebbles,  from  five  to  ten 
inches  long,  three  to  six  inches  wide,  set  on  end  in  a  bed  of 
sand  or  fine  gravel,  and  firmly  settled  in  place  by  pounding 
with  a  heavy  rammer.     A.f ter  the  stones  are  driven,  the  road- 
surface  is  covered  with  a  layer  of  clean  sand  or  gravel,  two 
or  three  inches  thick. 

The  objections  to  this  pavement  are  its  roughness;  the 
resistance  offered  to  the  wheels ;  the  noise ;  the  ease  with 
which  holes  are  formed  in  the  road  by  the  stones  being  pressed 
down  in  the  ground  by  heavy  loads  passing  over  them ;  the 
difficulty  of  cleaning  its  surface ;  and  its  need  of  frequent 
repairs. 

574.  Kind  of  stones  used  for  pavements. — The  fine-grained 

franites  which  contain  but  a  small  proportion  of  mica,  and  the 
ne-grained  silicious  sand-stones  which  are  free  from  clay, 
form  good  material  for  blocks  for  paving.  Mica  slate,  talcose 
slate,  hornblende  slate,  some  varieties  of  gneiss,  and  some 
varieties  of  sand-stone  of  a  slaty  structure,  yield  excellent 
materials  for  pavements  for  sidewalks  and  paths. 


VI.    ROADS   OF   OTHER   MATERIALS. 

575.  "Wooden  blocks  have  been  much  used  recently  in 
paving  the  streets  of  our  towns  and  cities.  Brick,  concrete, 
asphalte,  and  even  cast  iron,  are  or  have  been  used  for  road- 
coverings.  Roads  near  blast-furnaces  are  frequently  seen 
covered  with  the  slag  from  the  furnaces,  and  those  near  kilns 
where  cement  is  burned,  with  cinders  and  clinkers  from 
the  kilns.  Road-coverings  of  charcoal  have  been  tried  in 
Michigan  and  Wisconsin. 

The  wooden,  brick,  and  asphaltic  pavements  are  the  most 
common  of  these. 

Wooden  pavements. — Wooden  pavements  are  the  same 
in  principle  as  stone.  The  road-bed  is  formed  and  the 
blocks  of  wood  are  placed  in  contact  with  each  other  upon 
the  surface  of  the  road-bed  as  described  for  the  blocks  of 
fltone  pavements.  The  wooden  blocks  are  parallelopipedons 


424  CIVIL   ENGINEERING. 

in  form  and  are  laid  with  the  grain  of  the  wood  in  the  direc- 
tion of  the  depth  of  the  road.  From  slight  differences  in  the 
details  of  construction  of  wooden  pavements  there  has  arisen 
quite  a  variety  of  names,  as  the  Nicolson,  the  bastard  Nicolson, 
the  Stowe,  the  Greeley,  the  unpatented,  etc.,  all  using  the 
wooden  blocks,  but  differing  slightly  in  other  ways. 

Wooden  pavements  offer  a  smooth  surface ;  are  easily 
kept  clean ;  not  noisy ;  easy  for  the  horses  and  vehicles ; 
pleasant  to  ride  upon ;  and  are  cheaper  at  first  cost  than 
stone  pavements.  For  these  reasons  they  have  been  much 
used  in  the  United  States. 

They  are,  however,  slippery  in  wet  weather ;  soon  wear  out ; 
and  unfit  for  roads  or  streets  over  which  there  is  a  heavy  travel. 
True  economy  forbids  their  use  except  as  temporary  roads. 

576.  Asphaltic  coverings. — Asphaltic  roads  may  be  com- 
posed of   broken  stone  and  this  covered  with  asphaltic  con- 
crete, or  the  broken  stone  covered  with  ordinary  concrete  and 
this  overlaid  with  a  covering  of  asphalte  mixed  with  sand. 
Asphaltic  roads  present  a  smooth  surface  which  does   not 
become  slippery  by  wear ;  a  surface  free  from  dust  and  mud  ; 
not  noisy ;  and  from  its  imperviousness  to  moisture  forms 
an  excellent  covering  over  the  road-bed  beneath  and  prevents 
the  escape  of  noxious  vapors  from  below. 

Asphaltic  roads  properly  made  are  growing  steadily  in 
favor  and  when  they  are  better  known  will  be  more  generally 
adopted  for  all  streets  in  towns  and  cities,  over  which  the 
travel  is  light. 

VH.   TRAM-ROADS. 

577.  In  order  that  the  tractive  force  should  be  a  minimum, 
the  resistance  offered  to  the  wheels  of  the  carriage  should  be 
a  minimum.     In  other  words,  the  harder  and  smoother  the 
road,  the  less  will  be  the  tractive  force  required.     But  car- 
riages drawn  by  horses  require  that  the  surface  of  the  road 
should  be  rough,  to  give  a  good  foothold  to  the  horses'  feet. 
These  two  opposite  requirements  are  united  only  in  roads 
with  track-ways,  on  which  there  are  at  least  two  parallel 
tracks  made  of  some  hard  and  smooth  material  for  the  wheels 
to  run  upon,  while  the  space  between  the  tracks  is  covered 
with  a  different  material  suitable  for  the  horses'  feet.     Con- 
structions of  this  class  are  termed  i:  tram-roads  "   or  "  tram- 
ways."    The  surface  of  the  tracks  or  "  trams  "  are  made  flush 
with  that  of  the  road  and  are  suitable  for  the  wheels  of  ordi- 
nary carriages.     Their  construction  will  be  alluded  to  in  the 
next  chapter. 


BECONNOISSANCE.  425 


CHAPTER   XXIL 

LOCATION  AND  CONSTRUCTION  OP  ROADS. 

578.  In  establishing  a  road  to  afford  means  of  communi- 
cation between  two  given  places,  there  are  several  points 
which  must  be  considered  by  the  engineer  and  those  inter- 
ested in  its  construction.  These  are  the  kind  of  road  to  be 
selected,  the  general  line  of  direction  to  be  chosen  or  located, 
and  the  construction  of  the  road. 

The  selection  of  the  kind  of  road  depends  upon  the  kind 
of  travel  which  is  to  pass  over  it ;  the  amount  of  travel,  both 
present  and  prospective ;  and  the  wants  of  the  community 
in  the  neighborhood  of  the  line.  The  location  and  construc- 
tion of  the  road  depend  upon  the  natural  features  of  the 
country  through  which  the  road  must  pass,  and  as  these  come 
exclusively  within  the  limits  of  the  engineer's  profession, 
they  alone  will  be  considered  in  this  chapter. 


LOCATION. 

579.  Reconnoissance. — The  examination  and  study  of  the 
country  by  the  eye  is  termed  a  reconnoissance,  and  is  usually 
made  in  advance  of  any  instrumental  surveys,  to  save  time 
and  expense.  The  general  form  of  the  country  and  the  ap- 
proximate position  of  the  road  may  frequently  be  determined 
by  it. 

A  careful  examination  of  the  general  maps  of  the  country, 
if  any  exist,  will  lessen  the  work  of  the  reconnoissance  very 
much,  as  by  this  the  engineer  will  be  able  to  discover  many 
of  the  features  which  will  be  favorable  or  otherwise  to  the 
location  of  the  road  in  their  vicinity. 

Roads  alon£  the  bank  of  a  large  stream  will  have  to  cross 
a  number  of  tributaries.  Roads  joining  two  important 
streams  running  nearly  parallel  to  each  other  must  cross  high 
ground  or  dividing  ridges  between  the  streams. 

An  examination  of  the  map  will  show  the  position  of  the 
streams,  and  from  these  the  engineer  may  trace  the  general 
directions  of  the  ridges,  determine  the  lowest  and  highest 
points,  and  obtain  the  lines  of  greatest  and  least  slopea 


4:26 


CIVIL   ENGINEERING. 


With  this  information  the  directions  of  the  roads  leading  from 
one  valley  to  another  may  be  approximately  located. 

It  is  seen  (Fig.  221)  that  if  A  and  B  are  to  be  joined  by  a 
road,  that  the  road  may  run  direct  from  A  to  B,  as  shown  by 
the  dotted  line  joining  them,  or  it  may  go,  by  following  the 


FIG.  221. 

general  directions  of  the  streams,  through  C,  as  shown  by  the 
dotted  line  A  C  B.  By  the  first  route,  the  road  would  be 
apparently  shorter,  but  the  ascents  and  descents  would  be 
greater ;  by  the  second,  the  road  would  be  longer,  but  the 
ascents  and  descents  more  gentle,  and  the  total  difference  of 
level  to  be  passed  over  would  be  less. 

We  can  draw  this  conclusion  from  the  fact  that  the  streams 
have  made  for  themselves  channels  which  follow  the  lines  of 
gentlest  slope.  And  that  if  two  streams  flow  in  the 


same 


direction,  the  high  ground  or  ridge  separating  them  has 
the  same  general  direction  and  inclination  as  the  streams. 
And  if  two  streams  approach  each  other  near  their  sources, 
as  those  at  C  in  the  figure,  that  this  indicates  a  depression  in 
the  main  ridge  in  this  vicinity. 

Hence  long  lines  of  road  usually  follow  the  valleys  of 
streams,  obtaining  in  this  way  moderate  grades  and  crossing 
the  ridges  by  the  lowest  passes. 

The  engineer  having  studied  thoroughly  the  map  and  made 
himself  acquainted  with  the  natural  features  of  the  country 
as  there  indicated,  proceeds  to  make  a  personal  examination 
of  the  ground,  to  identify  these  natural  features,  and  to  verify 
the  conclusions  deduced  from  the  study  of  the  map. 

In  making  the  examination,  he  goes  both  forwards  and 
backwards  over  the  ground  so  as  to  see  it  from  both  direc- 


ESTIMATE   OF   THE   COST.  4:27 

tions,  and  in  this  way  verify  or  correct  the  impressions  he  has 
received  as  to  its  nature. 

By  means  of  the  reconnoissance  he  establishes  "  approxi- 
mate "  or  "  trial  lines "  for  examination.  These  lines  are 
marked  out  by  "  blazing  "  if  in  a  wooded  country,  or  by  stout 
stakes  driven  at  the  important  points  if  the  country  be  a 
cleared  or  open  one. 

580.  Surveys. — The  surveys  are  divided  into  three  classes : 
preliminary  surveys,  surveys  of  location,  and  surveys  of  con- 
struction. 

The  preliminary  survey  is  made  with  ordinary  instru- 
ments, generally  a  transit  and  a  level,  and  has  for  its  object 
the  measurement  of  the  length  of  the  road,  the  changes  of 
direction  of  the  different  courses,  the  relative  heights  of  the 
different  points  or  differences  of  level  along  the  line,  and  of 
obtaining  the  topography  of  the  country  passed  over  in  the 
immediate  neighborhood  of  the  line. 

The  line  is  run  without  curves,  and  therefore,  when  plot- 
ted, consists  of  a  series  of  straight  lines  of  different  lengths, 
forming  at  their  connection  angles  of  varying  size. 

The  levelling  party,  besides  taking  the  measurements  re- 
quisite to  construct  a  profile  of  the  line,  make  cross-section 
levellings  at  suitable  points,  so  as  to  show  the  form  of  surface 
of  the  road. 

The  topography  on  each  side  of  the  line  is  ordinarily 
sketched  in  by  eye ;  instrumental  measurements  being  occa- 
sionally made  to  check  the  work. 

581.  Map  and  memoir. — The   results   of  these   surveys 
are   mapped,  and  all  the  information  gathered  during  the 
survey  which  cannot  be  shown  on  the  map  is  embodied  in  a 
memoir. 

From  these  trial  lines  thus  surveyed,  the  engineer  makes  a 
selection,  being  governed  by  the  considerations  mentioned  in 
Art.  567,  viz.,  shortness  of  route,  avoidance  of  unnecessary 
ascents  and  descents,  selection  of  favorable  grades,  and  econ 
omy  of  construction. 

582.  Estimate   of  the   cost.  —  This   can   be   made   ap- 
proximately after  the  engineer  has  established  the  grades. 

The  kind  of  road  and  the  character  of  the  travel  over  it 
generally  fix  the  limits  of  its  longitudinal  slopes.  To  fix 
them  exactly,  the  engineer  constructs  the  profiles  of  the  dif- 
ferent sections  of  the  road  and  draws  the  "grade  lines"  on 
these  profiles,  keeping  their  slopes  within  the  general  limit 
already  assumed.  Thus  in  a  profile  (Fig.  222)  the  grade 
line  A  "B  is  drawn,  following  the  mean  or  general  slope  of  the 
ground,  equalizing  as  far  as  possible  the  undulations  of  tho 


428 


CIVIL   ENGINEERING. 


profile  above  and  below  the  grade  line.  The  inclination  of 
the  grade  line  with  the  horizontal  is  then  measured,  and  if  its 
slope  falls  within  the  limit  assumed,  the  grade  is  a  satisfactory 
one  and  the  amounts  of  excavation  and  embankment  are 
nearly  equal.  If  the  inclination  be  found  too  steep,  either 


FIG.  222. 


the  top  of  the  hill  must  be  cut  down  or  the  length  of  the  line 
between  the  two  points  at  top  and  bottom  be  increased.  The 
latter  is  the  method  usually  adopted.  Thus  if  the  road  laid 
out  on  a  straight  line  joining  C  and  D  (Fig.  223)  requires  a 


\ 


FIG.  223. 

steeper  grade  than  the  maximum  grade  adopted,  the  length 
of  the  road  between  these  points,  C  and  D,  may  be  increased 
by  curving  it,  as  shown  by  the  line  C  E  F  D.  The  length  to 
give  this  winding  road  is  easily  determined  so  that  the  grade 
of  every  portion  of  the  road  shall  be  kept  within  the  assumed 
limit.  The  proper  grade  line  having  been  determined  and 
drawn  on  the  profiles,  the  height  of  the  embankments  and 
the  depth  of  the  cuttings  are  determined. 

Knowing  the  width  of  the  road,  the  form  of  its  surface, 
and  the  inclination  of  the  side  slopes,  the  cubical  contents  of 
the  excavations  and  embankments  may  be  calculated,  and  an 
estimate  of  the  cost  made. 

The  comparative  costs  of  the  routes  being  determined  and 
the  considerations  mentioned  in  last  article  given  their  full 
weight,  the  engineer  selects  the  particular  line  for  the  road. 

It  is  well  to  say  that  it  happens  often  that  no  trial  lines 


SURVEYS.  429 

are  necessary ;  the  route  to  be  followed  by  the  road  being 
apparent. 

583.  Survey  of  location. — The  route  being  selected,  it  is 
gone  over  again  and  more  accurately  surveyed.     It  is  care- 
fully levelled  at  regular  intervals  in  the  direction  of  its  length, 
and  cross-levels  at  all  important  points  are  made.     The  angles 
made  by  the  changes  of  direction  of  the  line  are  rounded  off 
by  curves,  the  curves  being  generally  arcs  of  circles.    Ad- 
vantage is  taken  of  this  survey  to  place  the  line  in  its  best 
position  so  as  to  reduce  to  a   minimum  the   embankments 
and  excavation,  and  to  give  the  best  approaches  to  the  points 
where  streams  are  to  be  crossed. 

The  line  is  divided  into  a  number  of  divisions,  and  maps  of 
these  divisions  are  made  showing  the  road  in  plan  and  the 
longitudinal  and  cross-sections  of  the  natural  ground,  with 
the  horizontal  and  vertical  measurements  written  upon  them. 

By  these  maps,  the  engineer  can  lay  out  the  line  on  the 
ground  and  can  determine  the  amount  of  excavation  and 
embankment  required  for  each  division. 

Besides  these  maps,  detailed  drawings  of  the  road-covering, 
of  the  bridges,  culverts,  drains,  etc.,  with  the  written  specifi- 
cations explaining  how  the  work  on  each  must  be  done,  should 
be  prepared. 

The  work  is  now  in  the  condition  that  estimates  of  its  cost 
can  be  accurately  made  and  its  construction  begun. 

584.  Survey  of  construction, — The  road  is  constructed 
by  contract  or  "  day  labor."     Whichever  method  is  adopted, 
it  is  first  necessary  to  "  lay  out  the  work."     This  laying  out 
the  work  forms  the  third  class  of  surveys,  or  survey  of  con- 
struction. 

From  the  maps  showing  the  location,  the  engineer  proceeds 
to  mark  out  the  axis  of  the  road  upon  the  ground  by  means 
of  stout  pegs  or  stakes  driven  at  equal  intervals  apart,  using  a 
transit  or  theodolite  to  keep  them  in  the  proper  line.  These 
stakes  are  numbered  to  correspond  with  the  same  points  indi- 
cated on  the  map. 

The  width  of  the  roadway  and  the  lines  on  the  ground 
corresponding  to  the  side  slopes  of  the  excavations  and  em- 
bankments, are  laid  out  in  the  same  manner,  by  stakes  placed 
along  the  lines  of  the  cross  profiles. 

Besides  the  numbers  marked  on  the  stakes,  to  indicate  their 
position  on  the  map,  other  numbers,  showing  the  depth  of  the 
excavations,  or  the  height  of  the  embankments  from  the  sur- 
face of  the  ground,  accompanied  bv  the  letters  Cut.  Fill.'  to 
indicate  a  cutting,  or  a  filling,  as  the  case  may  be,  are  also 
added  to  guide  the  workmen.  The  positions  of  the  stakes  on 


430  CIVIL   ENGINEERING. 

the  ground,  which  show  the  principal  points  of  the  axis  of  the 
road,  should  be  laid  down  on  the  map  by  bearings  and  dis- 
tances from  bench-marks  in  their  vicinity,  in  order  that  the 
points  may  be  readily  found  should  the  stakes  be  subsequently 
misplaced. 

Curves.— Curves  are  not  necessary  for  common  roads,  but 
it  always  looks  better  even  in  a  common  road  to  join  two 
straight  portions  by  a  regular  curve  than  by  a  bent  line. 

Curves  are  laid  out  by  means  of  offsets  from  a  chord  or  tan- 
gent, or  by  angles  of  deflection  from  the  tangent.  The  latter 
method,  using  a  transit  or  theodolite,  is  the  one  most  com- 
monly employed. 

CONSTRUCTION. 

585,  Earth-work. — This  term  is  applied  to  all  that  relates 
to  the  excavations  and  embankments,  whatever  be  the  mate- 
rial excavated  or  handled. 

Excavations. — In  forming  the  excavations,  the  inclination 
of  the  side  slopes  demands  particular  attention.  This  incli- 
nation will  depend  on  the  nature  of  the  soil,  and  the  action  of 
the  atmosphere  and  internal  moisture  upon  it.  In  common 
soils,  as  ordinary  earth  formed  of  a  mixture  of  clay  and  sand, 
hard  clay,  and  compact  stony  soils,  although  the  side  slopes 
would  withstand  very  well  the  effects  of  the  weather  with 
a  greater  inclination,  it  is  best  to  give  them  a  slope  of  -J ; 
as  the  surface  of  the  roadway  will,  by  this  arrangement,  be 
better  exposed  to  the  action  of  the  sun  and  air,  which  will  cause 
a  rapid  evaporation  of  the  moisture  on  the  surface.  Pure 
sand  and  gravel  require  a  slope  of  -J.  In  all  cases  where  the 
depth  of  the  excavation  is  great,  the  base  of  the  slope  should 
be  increased.  It  is  not  usual  to  use  artificial  means  to  protect 
the  surface  of  the  side  slopes  from  the  action  of  the  weather ; 
but  it  is  a  precaution  which,  in  the  end,  will  save  much  labor 
and  expense  in  keeping  the  roadway  in  good  order.  The 
simplest  means  which  can  be  used  for  this  purpose,  consist  in 
covering  the  slopes  with  good  sods,  or  else  with  a  layer  of 
mould  about  four  inches  thick,  and  sown  with  grass-seed. 
These  means  will  be  amply  sufficient  to  protect  the  side 
slopes  from  injury  when  they  are  not  exposed  to  any  other 
causes  of  deterioration  than  the  wash  of  the  rain  and  the 
action  of  frost  on  the  ordinary  moisture  retained  by  the  soil. 

The  side  slopes  form  usually  an  unbroken  surface  from  the 
foot  to  the  top.  But  in  deep  excavations,  and  particularly  in 
soils  liable  to  slips,  they  are  sometimes  formed  with  horizontal 
offsets,  termed  benches,  which  are  made  a  few  feet  wide  and 


EMBANKMENTS.  431 

have  a  ditch  on  the  inner  side  to  receive  the  surface-water 
from  the  portion  of  the  side  slope  above  them.  These  benches 
catch  and  retain  the  earth  that  may  fall  from  the  portion  of 
the  side  slope  above. 

In  excavations  through  solid  rock,  which  does  not  disinte- 
grate on  exposure  to  the  atmosphere,  the  side  slopes  might  be 
made  perpendicular ;  but  as  this  would  .exclude,  in  a  great 
degree,  the  action  of  the  sun  and  air,  which  is  essential  to 
keeping  the  road-surface  dry  and  in  good  order,  it  will  be 
necessary  to  make  the  side  slopes  with  an  inclination,  varying 
according  to  the  locality ;  the  inclination  of  the  slope  on  the 
south  side  in  northern  latitudes  being  greatest,  to  expose  bet- 
ter the  road-surface  to  the  sun's  rays. 

Embankments. — In  forming  the  embankments,  the  side 
slopes  should  be  made  less  than  the  natural  slope  ;  for  the  pur- 
pose of  giving  them  greater  durability,  and  to  prevent  the  width 
of  the  top  surface  along  which  the  roadway  is  made  from 
diminishing  by  every  change  in  the  side-slopes,  as  it  would 
were  they  made  with  the  natural  slope.  To  protect  more 
effectually  the  side-slopes,  they  should  be  sodded  or  sown  in 
grass  seed ;  and  the  surface-water  of  the  top  should  not  be 
allowed  to  run  down  them,  as  it  would  soon  wash  them  into 
gullies  and  injure  the  embankment.  In  localities  where 
stone  is  plenty,  a  retaining  wall  of  dry  stone  may  be  advan- 
tageously substituted  for  the  side-slopes. 

To  reduce  the  settling  which  takes  place  in  embankments, 
the  earth  should  be  laid  in  successive  layers,  and  each  layer 
well  settled  with  rammers.  As  this  method  is  expensive,  it 
is  seldom  resorted  to  except  in  works  which  require  great 
care,  and  are  of  small  extent.  For  extensive  works,  the 
method  usually  adopted  is  to  embank  out  from  one  end,  carry- 
ing forward  the  rork  on  a  level  with  the  top  surface.  In 


FIG.  224. 

this  case,  as  there  must  be  a  want  of  compactness  in  the 
mass,  it  is  best  to  form  the  outsides  of  the  embankment 
tii-st,  and  to  gradually  fill  in  towards  the  middle,  in  order 
that  the  earth  may  arrange  itself  in  layers  with  a  dip 
towards  the  centre  (Fig.  224).  This  arrangement  will  in  a 


432  CIVIL  ENGINEERING. 

great  measure  counteract  the  tendency  of  the  earth  sliding 
off  in  layers  along  the  sides. 

586.  Removal  of  the  earth. — In  both  excavation  and 
embankment,  the  problem  is  "  to  remove  the  earth  from  the 
excavation  to  the  embankment  or  place  of  deposit  by  the 
shortest  distance,  in  the  shortest  time,  and  at  the  least 
expense."  This  is  an  important  problem  in  practice,  and 
its  proper  solution  affects  very  materially  the  cost  of  the 
work. 

The  average  distance  to  which  the  earth  is  carried  to  form 
the  embankment  is  called  the  lead,  and  is  assumed  to  be 
equal  to  the  right  line  joining  the  centre  of  gravity  of  the 
volume  of  excavation  with  that  of  the  embankment.  When 
this  lead  is  made  the  least  possible,  all  other  things  being 
equal,  the  cost  of  removal  of  the  earth  is  a  minimum. 

In  the  execution  of  earthwork,  it  is  not  always  advisable 
to  make  the  whole  of  an  embankment  from  the  adjoining 
cuttings,  as  the  lead  would  be  too  long.  In  such  a  case,  a 
part  of  the  cutting  is  wasted,  being  deposited  in  some  conve- 
nient place,  forming  what  is  known  as  a  spoil-bank.  The 
necessary  earth  required  to  complete  the  embankment  is 
obtained  from  some  spot  nearer  to  the  work,  and  the  cutting 
or  excavation  made  in  supplying  it  is  called  a  borrow-pit. 

Means  used  to  move  the  earth. — The  earth  is  loosened 
by  means  of  ploughs,  picks,  and  shovels,  and  then  thrown 
into  wheelbarrows,  carts,  or  wagons  to  be  removed.  A 
scraper  drawn  by  a  horse  is  frequently  used  to  great  advan- 
tage. 

Resort  is  sometimes  had  to  blasting  to  loosen  the  soil,  when 
it  is  rock,  hard  clay,  and  even  frozen  earth. 

The  advantages  of  wheelbarrows  over  carts,  and  carts  over 
wagons,  etc.,  depend  upon  circumstances.  When  the  earth 
is  to  be  transported  to  a  considerable  distance,  the  wheelbar- 
row becomes  too  expensive.  By  combining  the  cost  of  filling 
the  cart  or  wheelbarrow,  the  amount  removed,  and  the  time 
occupied  in  transporting  the  earth  in  each  case,  the  cost  of  the 
two  methods  can  be  obtained  and  compared  with  each  other. 

Shrinkage. — When  embankments  are  made  in  layers  com- 
pacted by  ramming  or  by  being  carted  over,  the  subsequent 
settling  is  quite  small.  But  made  in  the  usual  way,  there  ia 
always  a  certain  amount  of  settling  which  follows  and  which 
is  provided  for  by  making  at  first  the  embankment  a  few 
inches  higher  than  it  is  to  be.  Earth  occupies  a  less  space  in 
an  embankment  than  in  its  natural  state ;  that  is,  a  greater 
number  of  cubic  yards  of  excavation  is  required  to  form  an 
embankment  than  there  are  cubic  yards  in  its  voluma 

This  shrinkage  of  the  earths  is  about  as  follows  : 


SIDE-HILL  BOAD8.  433 

G  ravel  shrinks  about  eight  per  cent. 

Gravel  and  sand  nine  per  cent. 

Clay  and  clayey  earth  ten  per  cent 

Loain  and  light  earths  twelve  per  cent. 

On  the  contrary,  rock  occupies  more  space  when  broken 
up  than  it  does  in  its  natural  state,  the  percentage  of  its 
increase  in  volume  varying  with  the  way  the  fragments  are 
piled  together.  Carelessly  piled  its  increase  of  volume  was 
found  to  be  about  seventy-five  per  cent,  and  when  care- 
fully piled,  fifty  per  cent. 

587.  Methods  of  obtaining  the  quantities  to  be  exca- 
vated, etc. — In   comparing  the  costs  of   the  routes  or  for 
rough  estimates,  it  is   sufficiently  exact  to  take  a  number 
of  equidistant  profiles,   and    calculate    the    solid    contents 
between  each  pair,  either  by  multiplying  the  half  sum  of 
their  areas  by  the  distance  between  them,  or  else  by  taking 
the   profile   at  the    middle   point  between    each  pair,   and 
multiplying  its  area  by  the  same  length  as  before ;  the  first 
of  these*  methods  gives  too  large  a  result,  and  the  second  too 
small. 

Where  an  exact  estimate  is  to  be  made,  the  Prismoidal 
formula  (Mensuration,  p.  129)  should  be  used.  This  formula 
gives  the  exact  contents. 

588.  In  swamps  and  marshes. — When  the  embankment 
is  made  through  a  swamp  or  marsh,  many  precautions  are 
necessary. 

If  the  bog  is  only  three  or  four  feet  deep  and  has  a  hard 
bottom,  it  is  recommended  to  remove  the  soft  material  and 
build  the  embankment  on  the  hard  stratum. 

If  it  be  too  deep  to  remove  the  soft  material,  its  surface, 
provided  it  be  not  too  soft,  may  be  covered  with  some  sub- 
stance to  form  an  artificial  bed  for  the  embankment.  Kows 
of  turf  with  the  grassy  side  downward  have  been  used. 
Brushwood  has  also  been  tried.  %  • 

If  the  swamp  be  deep  and  the  material  quite  fluid,  the  first 
thing  to  do  is  to  drain  it,  and  then  prepare  an  artificial  bed 
for  the  embankment. 

589.  Side-tiill  roads. — When  a  road  runs  along  the  side 
of  a  hill,  it  is  usually  made  half  in  excavation  and  half  in 
embankment.     But  as  the  embankment  is  liable  to  slip  if 
simply  deposited  on  the  natural  surface  of  the  ground,  the 
latter  .should  be  cut  into  steps  or  offsets  (Fig.  225).     A  low 
stone  wall  constructed  at  the  foot  of  the  embankment  will  add 
to  its  stability. 

If  the  surface  of  the  hill  be  very  much  inclined,  the  side 
slopes  of  both  the  excavation  and  the  embankment  should  be 
28 


434 


CIVIL   ENGINEERING. 


replaced  by  retaining  walls  of  dry  stone  (Fig.  226),  or  of  stunes 
laid  in  mortar. 

The  upper  wall  may  be  dispensed  with  when  the  side  hill 
is  of  rock. 


FIG.  225. 

"When  the  road  passes  along  the  face  of  a  nearly  perpen- 
dicular precipice  at  a  considerable  height,  as  around  a  pro- 
jecting point  of  a  rocky  bank  of  a  river  in  a  mountainous 


FIG.  226. 


district,  it  may  rest  on  a  frame- work  of  horizontal  beams  let 
into  holes  drilled  in  the  face  of  the  precipice  and  supported 
at  their  outer  ends  by  inclined  struts  beneath,  the  lower  ends 
of  which  rest  in  notches  formed  in  the  rock. 


CROSS   DRAINS.  435 


DRAINAGE. 

590.  A  system  of  thorough  drainage,  by  which  the  water 
rrtat  filters  through  the  ground  will  be  cut  off  from  the  soil 
beneath  the  roadway,  to  a  depth  of  at  least  three  feet  below 
the  bottom  of  the  road-covering,  and  by  whic'i  the  water 
falling  upon  the  surface  will  be  speedily  conveyed  off,  before 
it  can  filter  through  the  road-covering,  is  essential  to  the  good 
condition  of  a  road. 

The  form  of  the  road,  the  side  drains,  and  the  ditches  (Fig 
218),  are  arranged  and  constructed  with  this  object  in  view 
(Art  556.)  •*«*.» 

591.  Covered  drains  or  ditches. — As  open  ditches  would 
be  soon  filled  by  the  washings  of  the  side-slopes  in  certain 
parts  of  the  roads,  covered  drains  (Fig.  227)  are  substituted 
ror  them  in  these  places. 


Fig.   227. 

They  may  be  constructed  with  a  bottom  of  concrete,  flag- 
ging, or  brick,  with  sides  of  the  same  material,  or  as  shown 
in  the  figure,  and  covered  with  flat  stones,  leaving  open  joints 
of  about  half  an  inch  to  give  free  admission  to  the  water.  The 
top  is  covered  with  brushwood  or  with  fragments  of  broken 
stone,  or  with  pebbles  and  clean  gravel,  through  which  the 
water  will  filter  freely  without  carrying  any  earth  or  sedi- 
ment into  the  drain. 

592.  Cross  drains. — Besides  the  covered  drains  parallel  to 
the  axis  of  the  road  in  cuttings,  other  drains  known  as  cross 
drains  are  made  under  the  roadway.  They  should  have  a 
slope  along  the  bottom  to  facilitate  the  escape  of  the  water. 
A  slope  of  1  in  100  will  be  sufficient. 

They  may  be  constructed  in  the  same  manner  as  the  cov- 
ered drains*  or  trenches  may  be  dug  to  the  required  depth 


436  CIVIL  ENGINEERING. 

with  the  proper  slope  and  filled  with  broken  stone.  On  the 
stone  a  layer  of  brushwood  is  placed  and  over  this  the  road- 
covering.  Drains  of  this  kind  are  known  as  blind  ditches. 
Any  construction  will  be  effective  which  will  leave  a  small 
open  waterway  at  the  bottom  of  the  trench  which  will  not  be- 
come choked  with  sediment. 

If  the  road  is  level,  the  cross  drains  may  run  straight  across, 
but  if  inclined  they  form  a  broken  line,  in  plan  the  shape  of 
the  letter  V,  with  the  angular  point  in  the  centre  of  the  road 
directed  towards  the  ascent.  From  their  form,  they  are 
termed  cross-mitre  drains. 

They  are  placed  at  intervals  depending  upon  the  nature 
of  the  soil  and  kind  of  road-covering  used,  in  some  cases  as 
much  as  sixty  yards  apart,  in  others  not  more  than  twenty 
feet. 

593.  Catchwaters. — These  are  broad  shallow  ditches  con- 
structed across  the   surface   of   the   road  so  arranged  that 
vehicles  can  pass  over  them  easily  and  without  shock.     They 
are  used  to  catch  the  water  which  runs  down  the  length  of 
the  road  and  to  turn  it  off  into  the  side  ditches.     They  are 
sometimes  called  water-tables. 

They  are  necessary  on  long  slopes,  and  in  depressions  where 
a  descent  and  an  ascent  meet,  to  prevent  the  water  from  cut- 
ting the  surface  of  the  road  in  furrows.  In  a  depression,  they 
are  usually  placed  at  right  angles  to  the  road  ;  on  a  slope,  they 
cross  the  road  diagonally  where  the  water  is  to  be  carried  to 
one  side  ;  if  to  both  sides,  their  plan  is  that  of  a  V  with  the 
angular  point  up  the  road. 

The  inclination  of  the  bottom  of  the  catch  water  should  be 
sufficient  to  carry  off  the  water  as  fast  as  it  accumulates  in 
the  trench,  and  where  the  velocity  of  the  current  flowing 
through  them  is  considerable,  they  should  be  paved. 

A  mound  of  earth  crossing  the  road  obliquely  is  frequently 
used  as  a  substitute  for  the  catchwater.  When  used  it  should 
be  arranged  to  allow  carriages  to  pass  over  them  without 
difficulty  and  inconvenience. 

594.  Culverts. — These  structures  are  used  to  carry  under 
the  road  the  water  of  small  streams  which  intersect  it,  and 
also  the  water  of  the  ditches  on  the  upper  side  of  a  road  to 
the  lower  side,  or  side  on  which  the  natural  water-courses  lie 
by  which  the  water  is  finally  carried  away. 

They  may  be  built  of  stone,  brick,  concrete,  or  even  of 
wood. 

Where  stone  is  scarce,  a  culvert  may  be  built  of  planks  or 
slabs,  forming  a  long  box  open  at  the  ends.  This  is  a  tern* 
porary  structure  unless  it  can  be  kept  always  wet. 


SIDEWALKS.  437 

A  small  full-centre  arch  of  brick  resting  on  a  flooring  of 
concrete  forms  a  good  culvert. 

The  length  of  a  culvert  under  an  embankment  will  be 
equal  to  the  width  of  the  road  increased  by  the  horizontal 
distance  on  each  side  forming  the  base  of  the  side-slope.  At 
each  end,  wing-walls  should  be  built,  their  faces  having 
the  same  slope  as  that  of  the  embankment.  The  ends  of  the 
culvert  must  be  protected  against  the  undermining  action  of 
the  water. 

The  form  of  cross-section  varies  according  to  the  circum- 
stances of  the  case,  depending  greatly  on  the  strength  required 
in  the  structure  and  the  volume  and  velocity  of  the  water 
flowing  through  it.  The  dimensions  of  the  waterway  of  a 
culvert  should  be  proportioned  to  the  greatest  volume  of 
water  which  it  may  ever  be  required  to  carry  off,  and  should 
always  be  large  enough  to  allow  of  a  person  entering  it  to 
clean  it  out. 

595.  Footpaths  and  sidewalks. — Ordinarily,  footpaths 
are  not  provided  for  in  our  country  roads.     They  should  be, 
however,  and  the  remarks  made  in  Art.  575  apply  to  their 
construction. 

In  cities  and  towns,  sidewalks  and  crossings  are  arranged 
in  all  the  streets.  They  are  made  of  flagging-stone,  brick, 
wood,  ordinary  concrete,  asphaltic  concrete,  etc.  They 
differ  in  construction  only  in  degree  from  roads  of  the  same 
kind. 

596.  Sidewalk  of  flagging-stone. — The  flagstones  are  at 
least  two  inches  in  thickness,  laid  on  a  bed  of  gravel.     The 
width  of  the  sidewalk  depends  upon  the  numbers  liable  to 
use  them,  being  wider  where  great  crowds  are  frequent  and 
less  wide  on  streets  not  much  used.     A  width  of  twelve  feet 
is  sufficient  for  most  cases. 

The  upper  surface  is  not  level,  but  has  a  slight  slope  to- 
wards the  street  to  convey  the  surface  water  to  the  side 
channels. 

The  pavement  of  the  street  is  separated  from  that  of  the 
sidewalk  by  a  row  of  long  slabs  set  on  their  edges,  termed 
curb-stones,  which  confine  both  the  flagging  and  paving 
stones.  The  curb-stones  form  the  sides  of  the  side  channels, 
and  should  for  this  purpose  project  six  inches  above  the  out- 
side paving  stones,  and  be  sunk  at  least  four  inches  below 
their  top  surface ;  they  should  be  flush  with  the  upper  sur- 
face of  the  sidewalks,  to  allow  the  water  to  run  over  into  the 
side  channels,  and  to  prevent  accidents  from  persons  tripping 
by  striking  their  feet  against  them. 

The  crossings  should  be  from  four  to  six  feet  wide,  and  be 


438  CIVIL   ENGINEEEING. 

slightly  raised  above  the  general  surface  of  the  pavement,  to 
keep  them  free  from  mud. 


TEAM-KOADS. 

Tram-roads  are  built  of  stone,  of  wood,  or  of  iron. 

597.  Stone  tram-roads.  —  The  best  tram-roads  of  stone 
consist  of  two  parallel  rows  of  granite  blocks,  about  4|-  feet 
apart  from  centre  to  centre,  the  upper  surface  of  the  blocks 
being  flush  with  the  surface  of  the  road.     The  blocks  should 
be  from  4  to  6  feet  long,  10  to  12  inches  broad  and  8  to  12 
inches  deep.     Sometimes  the  upper  surface  is  made  slightly 
concave  for  the  purpose  of  retaining  the  wheels  on  the  tracks. 

Stone  tram-roads  were  used  by  the  Egyptians,  traces  of 
them  being  found  in  the  quarries  which  supplied  stone  for  the 
pyramids. 

Tram-roads  of  stone  have  been  used  in  England,  and  are 
used  at  the  present  time  in  Italy. 

The  granite  blocks  used  in  the  Italian  tram-roads  are  from 
4  to  6  feet  long,  about  2  feet  broad,  and  8  inches  deep,  laid  on 
a  bed  of  gravel  6  inches  thick.  The  space  between  the 
"  trams  "  is  paved  with  cobble  stones  with  an  inclination  from 
the  outside  to  the  middle  line.  The  centre  is  therefore  lower 
than  the  sides,  forming  a  channel  for  the  water,  which  flows 
into  cross  drains  provided  to  carry  it  off. 

In  a  tram-road  on  the  Holy  head  road,  the  granite  blocks 
were  required  to  be  not  less  than  4  feet  long,  14  inches  broad, 
and  12  inches  deep.  The  blocks  were  laid  on  a  bed  composed 
of  a  rough  sub-pavement,  similar  to  that  used  for  the  Telford 
road,  on  which  was  a  layer  three  inches  thick  of  small  broken 
stone,  and  on  top  of  this  a  layer  of  gravel  two  inches  thick, 
compacted  by  a  heavy  roller. 

The  effect  of  this  tram-road  was  to  reduce  the  required 
amount  of  tractive  force  to  less  than  one-half  of  what  was 
required  on  the  broken  stone  road. 

598.  Tram-roads  of  wood. — Where  timber  is  plenty,  tram- 
roads  of  wood  are  frequently  used.     They  do  not  differ  in 
principle  of  construction  from  the  stone  tramway.     Since  the 
wood   is   extremely   perishable   when   buried   in   the   damp 
ground,  tramways  of  wood  are  used  only  in  temporary  con- 
structions. 

.  599.  Iron  tram-roads. — The  iron  tram-roads  formerly  used 
were  made  by  covering  a  wooden  track  with  flat  iron  bars,  so  as 
to  increase  the  durability  of  the  track  and  to  lessen  the  resist- 
ance offered  to  the  wheels.  To  keep  the  wheels  on  the  track,  a 


RAILROADS.  4:39 

flange  was  placed  on  the  side  of  the  bar  (Fig.  228).  The 
objections  to  these  tramways  were  that  the  broad  surface  cf 
the  iron  plate  collected  obstructions  upon  it,  and  that  the  fric- 
tion of  the  wheels  against  the  flange  was  very  great. 


FIG.  238.  FIG.  229. 

An  iron  plate  (Fig.  229)  is  used  quite  extensively  in  the 
United  States,  particularly  in  Philadelphia,  for  tracks  for 
street  cars.  The  upper  and  narrower  portion  is  used  by  the 
wheels  of  the  car,  while  the  wider  and  flat  portion  can  be 
used  by  ordinary  carriages. 


CHAPTER  XXEEL 

RAILROADS. 

600.  As  long  as  the  flange  attached  to  the  bar  was  used  to 
keep  the  wheels  on  the  track,  the  road  was  called  a  tram-road. 
When  the  flange  was  removed  from  the  bar  and  transferred 
to  the  wheel,  the  road  became  changed  in  character  and  was 
named  a  railway  or  railroad.     The  marked  difference  be- 
tween a  tram-road  and  a  railroad  is,  that  the  former  is  used  by 
all  classes  of  carriages,  while  the  latter  can  be  used  only  by 
cars  specially  built  tor  the  purpose. 

A  railroad  may  be  defined  to  be  a  track  formed  of  iron  or 
steel  bars,  called  rails,  placed  in  parallel  lines,  and  upon 
which  the  wheels  of  vehicles  run. 

The  general  principles  already  alluded  to  as  governing  the 
location  and  construction  of  roads,  apply  equally  to  railroads, 
but  in  a  higher  degree.  Greater  importance  is  attached,  for 
railroads,  to  straightness,  to  easy  grades,  and  to  using  curves 
of  larger  radius  where  a  change  of  direction  takes  place,  than 
for  any  other  kind  of  road. 

601.  Direction. — Straightness  of  direction  is  more  import- 


440  CIVIL   ENGINEERING. 

ant  for  railroads  than  for  common  roads,  for  the  reasons  that 
the  shorter  the  line  the  cheaper  is  its  cost,  and  that  there  i8 
a  greater  resistance  offered  by  curves,  causing  a  greater  ex- 
penditure of  tractive  force. 

The  same  considerations  which  govern  in  determining  the 
direction  of  a  common  road  apply  to  the  railroad,  viz.,  cost  of 
construction,  wants  of  the  community,  etc. 

602.  Grades. — The  question  of  grade  is  more  one  of 
economy  than  of  practicability.  Locomotives  can  be  made 
to  ascend  steep  grades  by  increasing  their  power  and  adhesion, 
but  as  the  grades  increase  in  steepness,  the  effective  tractive 
force  of  the  engine  decreases.  Thus  with  an  ascent  of  20 
feet  to  the  mile,  an  engine  can  draw  about  one-half  the  load 
which  it  can  draw  on  a  level ;  with  40  feet  to  the  mile,  about 
one-third,  etc. 

The  cost  of  drawing  a  load  on  a  railroad  varies  very  nearly 
with  the  power  employed.  Hence  it  will  cost  nearly  twice  as 
much  to  haul  a  load  on  a  grade  of  20  feet  to  the  mile  as  it 
would  on  a  level  road.  This  consideration  will  therefore 
justify  large  expenditures  in  the  construction  of  the  road  if 
made  with  the  view  of  reducing  the  grades. 

The  ruling  or  maximum  grade  adopted  for  the  line  depends 
upon  the  motive  power  used  to  ascend  the  grades  and  upon 
the  avoidance  of  a  waste  of  power  in  descending. 

The  steepest  grade  upon  a  given  line  is  not  necessaiily  the 
maximum  inclination  adopted  for  the  road.  It  may  be  much 
greater  than  the  ruling  grade,  and  will  then  require  special 
arrangements  to  be  made  to  overcome  it. 

When  the  loads  to  be  carried  in  one  direction  over  the  road 
are  much  heavier  than  those  carried  in  the  other,  the  ascent 
up  which  the  heavy  loads  are  to  be  carried  should  be  made  by 
easy  grades,  while  the  descent  may  be  made  by  steeper  ones. 
If  the  travel  is  equal  in  both  directions,  the  ruling  grades 
should  be  equal  for  both  slopes. 

The  length  of  grades  must  be  considered,  as  it  is  found 
more  advantageous  to  have  steep  grades  upon  short  portions 
of  the  line  than  to  overcome  the  same  difference  of  level  by 
grades  not  so  steep  on  longer  developments. 

From  various  experiments,  it  appears  that  the  angle  of 
repose  (Art.  550)  for  a  railroad  is  about  -^fa.  But  in  de- 
scending grades  much  steeper  than  this,  the  velocity  due  to 
the  accelerating  force  of  gravity  soon  attains  its  greatest 
limit  and  remains  constant,  from  the  resistance  caused  by  the 
air. 

The  limit  of  the  velocity  thus  attained,  whether  the  train 


CURVES.  441 

descends  by  the  action  of  gravity  alone,  or  by  the  combined 
action  of  the  motive  power  of  the  engine  and  gravity,  can  be 
determined  for  any  given  load.  It  appears  from  calculation 
and  experiment  that  heavy  trains,  allowed  to  run  freely 
without  applying  the  brakes,  may  descend  grades  of  T^  with- 
out attaining  a  greater  velocity  than  about  40  miles  an  hour. 

Hence,  the  question  to  be  considered  in  comparing  the 
advantages  of  different  grades  is  one  between  the  loss  of  power 
and  speed  for  ascending  trains  on  steep  grades,  and  the  extra 
cost  of  heavy  excavations,  tunnels,  and  embankments  required 
by  lighter  grades. 

Since  locomotives  are  not  taxed  to  their  full  extent,  grades 
of  60  feet  to  the  mile  may  be  used  without  any  practical  loss 
of  power  either  in  the  ascent  or  descent. 

603.  Curves. — Curves  are  necessary  to  enable  the  road  to 
pass  around  obstacles,  such  as  hills,  deep  ravines,  valuable 
houses  which  cannot  be  removed,  etc. 

The  objections  to  curves  in  the  road  are  the  resistances 
which  they  offer  to  the  motion  of  the  cars  and  the  dangers  to 
which  the  cars  are  exposed. 

The  resistances  offered  by  the  curves  are  chiefly  due  to  the 
following  causes : 

1.  The  obliquity  of  the  moving  power  while  passing  around 
the  curve. 

2.  The  friction  of  the  flanges  of  the  wheels  against  the 
outer  rail  due  to  the  centrifugal  force. 

3.  The  friction  of  the  flanges  against  the  rails  due  to  the 
parallelism  of  the  axles. 

4.  The  fastening  of  each  pair  of  wheels  to  the  same  axle. 
The  danger  of  a  car  running  off  the  track  is  much  increased 

by  curves.  The  car  is  kept  on  the  rails  while  going  around 
a  curve  by  the  flanges  of  the  wheels  and  by  the  firmness  of  the 
outer  rails.  If  the  resistance  offered  by  the  rails  and  flanges 
should  be  overcome  by  the  "  quantity  of  motion  "  of  the  car, 
the  latter  would  leave  the  track.  Hence,  where  sharp  curves 
are  necessary,  they  should  be  located,  if  possible,  near  stop- 
ping places,  and  never  at  those  points  where  the  speed  is  to  be 
very  high  or  where  the  car  will  pass  with  great  velocity,  as 
at  the  foot  of  a  steep  grade. 

The  minimum  radius  of  a  curve  depends  greatly  upon  the 
Bpeed  to  be  employed.  In  France,  the  minimum  radius 
allowed  is  2,700  feet.  In  England,  no  curve  less  than  2,640 
feet  can  be  used  without  special  permission  of  Parliament  or 
the  Board  of  Trade.  The  minimum  radius  used  on  the  Hud- 
son River  Railroad  is  2,062  feet.  On  the  Baltimore  and  Ohio 
Railroad,  the  minimum  radius  is  600  feet,  although  when  first 


442  CIVIL   ENGINEERING. 

constructed  there  were  several  curves  of  400  feet  radius,  and 
one  of  318  feet  over  which  trains  passed  at  a  speed  of  15 
miles  an  hour. 

604.  Resistances  of  vehicles  on  railroads.  —  The  resist- 
ance offered  to  the  force  of  traction  by  a  train  of  cars  is  due 
to  friction,  concussion,  and  the  atmosphere.    The  amount 
of  this  resistance  depends  upon  a  variety  of  conditions,  such  as 
the  condition  of  the  road,  whether  well  or  badly  constructed, 
in  bad  order,  etc.  ;  the  state  of  the  rolling  machinery  ;  the 
climate  ;  the  season  of  the  year  ;  state  of  the  weather,  etc. 

In  discussing  the  resistance,  it  is  assumed  that  the  cars  are 
well  made,  the  track  in  good  order,  and  the  weather  moder- 
ately calm.  The  amount  of  resistance  may  be  determined  by 
means  of  a  dynamometer  between  the  engine  and  the  train, 
and  may  be  expressed  either  as  a  fraction  or  as  a  certain  num- 
ber of  pounds  per  ton,  the  latter  being  generally  used. 

That  part  of  the  resistance  offered  by  the  train  due  to 
friction  is  constant  at  all  speeds  ;  that  due  to  concussion  and 
the  atmosphere  varies  with  the  velocity,  increasing  with  the 
speed.  The  law  of  increase  is  not  fully  known. 

605.  On  a  level  and  straight  road.  —  The  resistance 
offered  by  a  train  running  on  a  level  and  straight  road,  nearly 
as  possible  under  the  conditions  in  ordinary  practice,  has  been 
determined  by  experiment  to  be  nearly  that  given   by   the 
following  formula  : 


in  which  r  is  the  resistance  in  pounds  per  ton  of  the  enginej 
tender,  and  train  ;  and  v  the  velocity  in  miles  per  hour. 

Hence  it  is  seen,  that  for  a  train  moving  at  the  rate  of  20 
miles  an  hour,  the  resistance  would  be  10.33  pounds  per  ton 
of  the  entire  train. 

If  the  road  is  in  bad  repair,  the  values  obtained  by  this 
formula  should  be  increased  40  per  cent.  ;  for  strong  side 
winds,  20  per  cent. 

606.  Resistance  due  to  grades.  —  The  resistance  due  to 
a  grade  is  found  by  multiplying  the  whole  weight  of  the  train 
by  the  difference  of  level  and  dividing  this  product  by  the 
length  of  the  slope.  By  this  rule  it  is  found  that  the  resist- 
ance per  ton  due  to  a  grade  of  24  feet  in  a  mile  is 

2,240  x  jr^  =  10.2  pounds, 

or  about  the  same  as  that  on  a  level  with  the  speed  of  20 
miles  an  hour.  Therefore,  if  the  train  runs  over  this  grade  at 


443 

20  inik-s  an  hour,  the  resistance  would  be  just  double,  or  it 
would  require  the  same  power  to  run  one  mile  on  the  grade 
that  would  draw  the  same  load  at  the  same  speed  two  miles 
on  a  level  road. 

607.  Resistance  due  to  curves.  —  The  resistance  due  to 
curvature  is  much  affected  by  the  gauge  of  the  road,  the  ele- 
vation of  the  outer  rail,  the  form  of  surface  of  the  tires  and 
the  size  of  the  wheels,  the  speed  and  length  of  the  train,  etc. 
Hence,  experiments  made  to  obtain  this  resistance  will  be 
found  to  vary  greatly  for  the  same  curve  on  different  roads. 
The  point  to  be  gained,  however,  is  to  find  the  amount  of 
curvature  which  will  consume  an  amount  of  power  sufficient 
to  draw  a  train  one  mile  on  a  straight  and  level  road. 

It  is  assumed  that  the  resistance  from  curvatur"e  is  inversely 
as  the  radius  ;  that  is,  the  resistance  offered  by  a  curve  of  2° 
is  double  that  of  a  curve  of  1°. 

From  experiments  made  under  his  direction,  Mr.  Latrobe 
deduced  the  resistance  upon  a  curve  of  400  feet  radius  to  be 
double  that  upon  a  straight  line. 

Upon  averaging  a  large  number  of  experiments  made  for 
this  purpose,  it  is  found  that  a  radius  of  574  feet,  or  curve  of 
10°,  offers  a  resistance  to  a  train  travelling  at  the  rate  of  20 
miles  an  hour,  double  that  on  a  straight  and  level  line,  at  the 
same  speed.  Hence  a  curve  of  ten  degrees  causes  a  resist- 
ance of  ten  pounds  to  the  ton.  Knowing  this  resistance,  that 
for  any  other  curve  is  easily  obtained. 

If  we  desire  to  make  the  resistance  uniform  upon  any  sys- 
tem of  grades  and  curves,  it  will  be  necessary,  whenever  a 
curve  occurs  upon  a  grade,  to  reduce  the  latter  to  an  amount 
sufficient  to  compensate  for  the  resistance  caused  by  the 
curve. 

608.  Mr.  Scott  Russell's  formula.  —  Formula  (173)  gives 
the  value  of  the  total  resistance  without  separating  it  into  its 
parts. 

The  formula  of  Mr.  Russell  and  Mr.  Harding  gives  separate 
expressions  for  each  resistance.  This  formula  is  as  follows  : 


,.    .    .(174) 


in  which  r  and  v  are  the  same  as  in  (173),  "W,  the  weight  of 
the  train  in  tons,  and  A,  the  area  of  rrontage  of  the  train  in 
square  feet. 

This  formula  may  be  expressed  in  words,  as  follows: 

1.  Multiply  the  weight  in  tons  by  6.     The  product  will  be 
the  amount  in  pounds  due  to  friction. 

2,  Multiply  the  weight  in  tons  by  the  velocity  in  miles  pei 


444  CIVIL   ENGINEERING. 

hour  and  divide  the  product  by  3.     The  result  will  be  the 
amount  in  pounds  due  to  concussion. 

3.  Multiply  the  square  of  the  velocity  in  miles  per  hour  by 
the  frontage  of  the  train  in  square  feet  and  divide  the  pro- 
duct by  400.     The  result  will  give  the  resistance  in  pounds 
due  to  the  atmosphere. 

4.  Add  these  three  results,  and  the  sum  is  the  total  resist- 
ance.   Divide  the  total  resistance  by  the  weight,  and  the  quo- 
tient is  the  resistance  per  ton. 

The  foregoing  results  corresponded  closely  with  the  experi- 
ments for  speed  from  30  to  60  miles  per  hour.  At  lower  rates 
of  speed,  the  rule  gave  too  great  results. 

Another  formula  has  been  used  in  which  the  resistance  of 
the  atmosphere  is  assumed  to  be  proportional  to  the  volume 
of  the  train.  It  is  as  follows  : 


in  which  13  is  the  volume  of  the  train,  the  other  quantities 
being  the  same  as  in  (174). 

609.  Tractive  force.  —  The  forces  employed  to  draw  the 
cars  on  railroads  are  gravity,  horses,  stationary  engines,  and 
locomotive  engines. 

610.  Gravity.  —  Gravity  either  assists  or  opposes  the  other 
kinds  of  motive  power  on  all  inclined  parts  of  a  railroad.     It 
may  be  used  as  the  sole  motive  power  on  grades  which  are 
sufficiently  steep.     In  this  case  the  loaded  cars  descending  the 
grade  draw  up  a  train  of  empty  ones.     The  connection  is 
made  between  the  trains  by  means  of  a  wire  rope  which  runs 
over  pulleys  placed  along  the  middle  of  the  track. 

611.  Horses.  —  Horses  are  frequently  used  to  draw  cars  on 
a  railroad. 

The  power  of  a  horse  to  move  a  heavy  load  is  ordinarily 
assumed  at  150  pounds,  moving  at  the  rate  of  2$  miles  an 
hour  for  8  hours  a  day.  At  greater  speeds  his  power  of 
draught  diminishes  ;  for  example  to  half  that  load  at  4  miles 
an  hour,  etc. 

The  power  of  the  horse  is  rapidly  diminished  upon  ascents. 
On  a  slope  of  1  in  7  (8J°)  he  can  carry  up  only  his  own 
weight  (Gillespie). 

612.  Stationary  engines,  —  These  are  employed  sometimes 
where  the  speed  is  to  be  moderate,  the  grade  steep,  and  the 
distance  short. 

The  power  is  usually  applied  by  means  of  an  endless  wire 
rope  running  on  pulleys,  like  that  employed  where  gravity 
is  the  only  motive  power.  And  as  in  that  case,  the  descent 


LOCOMOTIVE   ENGINES.  445 

of  one  train  is  generally  made  to  assist  in  the  drawing  up  of 
another  to  the  top  of  the  inclined  plane. 

613.  Locomotive  engines. — The  principal  motive  power 
on  railroads  is  the  locomotive  engine. 

The  locomotive  is  a  non-condensing,  righ-pressure  engine, 
working  at  a  greater  or  less  degree  or  expansion  according  to 
circumstances,  and  placed  on  wheels  which  are  connected 
with  the  piston  in  such  a  manner  that  any  motion  of  the  latter 
is  communicated  to  them. 

The  power  exerted  in  the  cylinder  and  transferred  to  the 
circumference  of  the  driving  wheel  is  termed  "  traction ; " 
its  amount  depends  upon  the  diameter  of  the  cylinder,  the 
pressure  of  the  steam,  the  diameter  of  the  driving  wheel,  and 
the  distance,  called  the  stroke,  traversed  by  the  piston  from 
one  end  of  the  cylinder  to  the  other. 

The  means  by  which  the  traction  is  rendered  available  for 
moving  the  engine  and  its  load  is  the  friction  of  the  driving 
wheels  on  the  rail ;  this  is  called  the  "  adhesion,"  and  its 
amount  varies  directly  with  the  load  resting  on  the  wheels, 
and  with  the  condition  of  the  surface  of  the  rails,  varying 
from  almost  nothing  when  ice  is  on  the  rails,  up  to  as  much 
as  one-fifth  of  the  weight  on  the  driving  wheels  when  the 
surface  of  the  rail  is  clean  and  dry. 

The  speed  of  the  engine  depends  also  upon  the  rapidity 
with  which  its  boiler  can  generate  steam.  One  cylinder  full 
of  steam  is  required  for  each  stroke  of  the  piston.  Each 
double  stroke  corresponds  to  one  revolution  of  the  driving 
wheels  and  to  the  propulsion  of  the  engine  through  a  space 
equal  to  their  circumference. 

Steam-production,  adhesion,  and  traction,  are  the  three 
elements  which  determine  the  ability  of  a  locomotive  engine 
to  do  its  work.  The  work  required  of  the  engine  depends 
upon  the  nature  and  amount  of  the  traffic  over  the  road  and 
the  condition  of  the  road.  Hence,  engines  of  different  pro- 
portions are  employed  on  the  same  road,  one  set  to  haul  heavy 
loads  at  low  velocities  and  another  set  to  move  light  loads  at 
high  rates  of  speed. 

Stronger  and  more  powerful  engines  are  needed  on  a  road 
with  steep  grades  and  sharp  curves  than  on  roads  with  easy 
grades  and  large  curves. 

Locomotive  engines  may  be  so  proportioned  as  to  run  at  any 
speed  from  0  to  60  miles  an  hour ;  to  ascend  grades  even  as 
Bteep  as  200  feet  in  the  mile ;  and  to  draw  from  1  to  1,000 
tone. 

The  weight  and  speed  of  the  trains,  and  the  ruling  grades 
of  the  road  determine  the  amount  of  power  required  of  the 


446  CIVIL    ENGINEERING. 

engine.  This  power  depends,  as  has  just  been  stated,  upon 
the  steam-producing  capacity  of  the  boiler,  upon  the  leverage 
with  which  the  steam  is  applied,  and  upon  the  adhesion. 

614.  Gauge. — The  width  of  a  railroad  between  the  innei 
sides  of  the  rails  is  called  the  gauge. 

The  question  as  to  what  this  width  should  be  has  been  a 
subject  for  discussion  and  of  controversy  among  engineers. 

The  original  railroads  were  made  of  the  same  width  as  the 
tram-roads  on  which  the  ordinary  road  wagon  was  used.  It 
happened  that  the  width  of  the  tram-road  was  4  feet  8-J-  inches ; 
this  was  adopted  for  the  railroad,  and  soon  became  universal. 
In  a  few  cases,  other  widths  were  adopted,  but  the  advantages 
of  uniformity  so  far  exceed  all  other  considerations,  that  the 
width  of  4  feet  8£  inches  is  now  generally  adopted  for  main 
lines  or  roads  of  the  first  class. 

For  branch  lines,  a  still  narrower  gauge  is  recommended  ; 
a  width  of  3  feet,  and  even  of  2  feet  6  inches,  has  been  em- 
ployed. A  road  of  this  narrow  gauge  costs  less  to  construct 
and  admits  of  steeper  grades  and  sharper  curves  being  used. 

Railroads  may  have  either  a  single  or  a  double  track. 
When  first  constructed  and  where  the  traffic  is  light,  a  single 
track  is  used,  but  even  then  it  is  recommended  to  secure 
ground  sufficient  for  a  second  track  when  the  latter  becomes 
necessary. 

The  New  York  Central  Railroad  has  four  tracks,  two  of 
which  are  used  for  passenger  traffic  and  two  for  movement 
of  freight. 

LOCATION   AND   CONSTRUCTION    OF   RAILROADS. 

615.  Location. — Location  of  railroads  is  guided  by  the  same 
principles  as  that  of  ordinary  roads  and  is  made  in  the  same 
manner.     The  greater  importance  to  railroads  of  easy  grades 
and  straightness  justifies  a  greater  expenditure  for  surveys, 
which  are  more  elaborate  than  those  required  for  common 
roads. 

616.  Construction. — This  may  be  divided  into  two  parts : 
forming  the  "  road-bed,"  and  the  "  superstructure." 

The  remarks  already  made  concerning  the  "  construction  of 
roads  "  apply  to  "  forming  the  road-bed  of  a  railroad." 

The  excavations  and  embankments  are  generally  much 
greater  on  railroads  than  for  any  other  of  the  roads  usually 
constructed.  Where,  for  instance,  an  ordinary  road  would 
wind  around  a  hill,  a  railroad  would  cut  through  it,  in  this 
way  obtaining  straightness  and  avoiding  curves. 

The  sides  of  an  excavation  are  often  supported  by  retain- 


SHAFTS   AND   TUNNELS.  4:47 

ing  walls  in  order  to  reduce  the  width  of  the  cutting  at  the 
top. 

617.  Tunnels. — When  the  depth  of   excavation   is   very 
great  it  will  frequently  be  found  cheaper  to  make  a  passage 
under  ground  called  a  tunnel. 

The  choice  between  deep  cutting  and  tunnelling  will  de- 
pend upon  the  relative  cost  of  the  two  and  the  nature  of  the 
ground.  When  the  cost  of  the  two  methods  would  be  about 
equal,  and  the  slopes  of  the  deep  cut  are  not  liable  to  slips,  it 
is  usually  more  advantageous  to  resort  to  deep  cutting  than  to 
tunnelling.  So  much,  however,  will  depend  upon  local  cir- 
cumstances, that  the  comparative  advantages  of  the  two 
methods  can  only  be  decided  by  a  careful  consideration  of 
these  circumstances  for  each  particular  case.  Where  a  choice 
may  be  made,  the  nature  of  the  ground,  the  length  of  the 
tunnel,  that  of  the  deep  cuts  by  which  it  must  be  approached, 
and  also  the  depths  of  the  working  shafts,  must  all  be  well 
studied  before  any  decision  can  be  made.  In  some  cases  it 
may  be  found  that  a  long  tunnel  with  short  deep  cuts  will  be 
most  advantageous  in  one  position,  and  a  short  tunnel  with 
long  deep  cuts  in  another.  In  others,  the  greater  depth  of 
working  shafts  may  be  more  than  compensated  for  by  the  ob- 
taining of  a  safer  soil,  or  a  shorter  tunnel. 

As  a  general  rule  tunnelling  is  to  be  avoided  if  possible. 

The  dimensions  and  form  of  the  cross-section  will  depend 
upon  the  nature  of  the  soil  and  the  object  of  the  tunnel  as  a 
communication.  In  solid  rock,  the  sides  of  the  tunnel  are 
usually  vertical,  the  top  curved,  and  the  bottom  horizontal. 
In  soils  which  require  to  be  sustained  by  an  arch,  the  exca- 
vation should  conform  as  nearly  as  practicable  to  the  form 
of  cross-section  of  the  arch. 

In  tunnels  through  unstratified  rocks,  the  sides  and  roof 
may  be  left  unsupported;  but  in  stratified  rocks  there  is 
danger  of  blocks  becoming  detached  and  falling :  wherever 
this  is  to  be  apprehended,  the  top  of  the  tunnel  should  be 
supported  by  an  arch. 

In  choosing  the  site  of  a  tunnel,  attention  should  be  had, 
not  only  to  the  nature  of  the  soil,  and  to  the  shortness  and 
straightness  of  the  tunnel,  but  also  to  the  facilities  offered  for 
getting  access  to  its  course  at  intermediate  points  by  means  of 
shafts  and  drifts. 

618.  Shafts. — Vertical  pits  which  are  sunk  to  a  level  with 
the  crown  or  top  of  the  tunnel  are  known  as  shafts. 

There  are  three  kinds :  trial,  -working,  and  permanent 
shafts. 

Trial  shafts  are,  in  general,  sunk  at  or  near  the  centre  line 


448  CIVIL  ENGINEERING. 

of  the  proposed  tunnel  to  ascertain  the  nature  of  the  strata 
through  which  the  tunnel  is  to  be  excavated.  Their  dimen- 
sions and  shape  are  regulated  by  the  uses  to  which  they  are  to 
be  put. 

Working  shafts  are  used  to  give  access  to  the  tunnel,  for 
the  purpose  of  carrying  on  the  work  and  removing  the  mate- 
rial excavated,  for  admitting  fresh  and  discharging  foul  air, 
and  for  pumping  out  water. 

Their  dimensions  will  be  fixed  by  the  service  required  of 
them.  Their  distance  apart  varies  between  50  and  300  yards, 
although  in  some  cases  they  are  only  from  20  to  30  yards 
apart,  and  in  others  none  are  used. 

They  may  be  located  along  the  centre  line  of  the  tunnel  or 
they  may  be  on  a  line  parallel  to  it. 

Permanent  shafts  are  generally  working  shafts  that  have 
been  made  permanent  parts  of  the"  tunnel  for  the  purposes  of 
ventilation  and  of  admitting  Jight. 

619.  Drifts.  —  Small  horizontal  or  slightly  inclined  under- 
ground passages  made  for  the  purpose  of  examining  the  strata, 
for  the  purpose  of  drainage,  of  affording  access  to  the  tunnel 
for   the  workmen  and  for  transport  of  materials,  etc.,  are 
termed  drifts  or  headings. 

Their  least  dimensions  are  those  in  which  miners  can  con- 
veniently work,  or  from  4f  to  5  feet  high  and  3  feet  wide. 

Headings  are  almost  always  used  to  connect  the  working 
shafts,  running  along  the  centre  line  or  parallel  to  the  line 
of  the  tunnel.  In  soft  ground,  the  heading  is  at  or  near  the 
bottom  of  the  tunnel ;  in  rock  or  hard  and  dry  material  at  or 
near  the  top. 

620.  Laying  out  tunnels. — The  establishment  of  a  correct 
centre  line  for  a  tunnel  and  the  fixing  of  the  line  at  the  bot- 
tom of  the  shafts  are  most  important  operations  and  require 
the  utmost  care. 

The  work  is  commenced  by  setting  out,  in  the  first  place, 
with  great  accuracy  upon  the  surface  of  the  ground,  the  pro- 
file line  contained  in  the  vertical  plane  of  the  axis  of  the 
tunnel,  and  at  suitable  intervals  along  this  line,  sinking  work- 
ing shafts.  At  the  bottom  of  these  shafts  the  centre  line  is 
marked  out  by  two  points  placed  as  far  apart  as  possible.  By 
these  the  line  is  prolonged  from  the  bottom  of  the  shaft  in 
both  directions. 

In  constructing  the  Hoosac  Tunnel,  so  accurate  were  the 
alignments,  that  the  heading  running  eastward  from  the 
central  shaft  for  a  distance  of  1,563  feet  met  the  heading 
from  the  eastern  end  with  an  error  of  but  five-sixteenths  of 
an  inch;  and  the  heading  running  westward  for  2,056  feet 


DBAINAGE   AND  VENTILATION.  449 

met  the  heading  from  the  western  end  with  an  error  of  but 
nine-sixteenths  of  an  inch. 

An  elaborate  trignometrical  survey  was  used  to  lay  out  the 
Mont  Cenis  Tunnel,  which  was  7.5  miles  long,  with  no  work- 
ing shafts. 

621.  Operation  of  tunnelling, — The  shafts  and  the  ex- 
cavations which  form  the  entrances  to  the  tunnel  are  con- 
nected by  a  drift,  usually  five  or  six  feet  in  width  and  seven 
or  eight  feet  in  height,  made  along  the  crown  of  the  tunnel 
when  the  soil  is  good.  After  the  drift  is  completed,  the 
excavation  for  the  tnnnel  is  gradually  enlarged ;  the  ex- 
cavated earth  is  raised  through  the  working  shafts,  and 
at  the  same  time  carried  out  at  the  ends.  The  speed  with 
which  the  drift  is  driven  determines  the  rate  of  progress  of 
the  whole. 

If  the  soil  is  loose,  the  operation  is  one  of  the  most  hazard- 
ous in  engineering  construction,  and  requires  the  greatest  pre- 
cautions against  accident.  The  sides  of  the  excavations  must 
be  sustained  by  strong  rough  frame- work,  covered  by  a  sheath- 
ing of  boards  to  secure  the  workmen  from  danger.  When  in 
such  cases  the  drift  cannot  be  extended  throughout  the  line 
of  the  tunnel,  the  excavation  is  advanced  only  a  few  feet  in 
each  direction  from  the  bottom  of  the  working  shafts,  and 
is  gradually  widened  and  deepened  to  the  proper  form  and 
dimensions  to  receive  the  masonry  of  the  tunnel,  which  is 
immediately  commenced  below  each  working  shaft,  and  is 
carried  forward  in  both  directions  towards  the  two  ends  of 
the  tunnel. 

In  some  cases,  two  headings  were  run  forward  and  the  side 
walls  of  the  tunnel  were  built  before  the  remainder  of  the 
section  was  excavated. 

The  ordinary  difficulties  of  tunnelling  are  greatly  increased 
by  the  presence  of  water  in  the  soil  through  which  the  work 
is  driven.  Pumps,  or  other  suitable  machinery  for  raising 
water,  placed  in  the  working  shafts,  will,  in  some  cases,  be 
requisite  to  keep  them  and  the  drifts  free  from  water  until  an 
outlet  can  be  obtained  for  it  at  the  ends,  by  a  drain  along  the 
bottom  of  the  drift. 

622.  Drainage  and  ventilation  of  tunnels. — The  drain- 
age of  a  tunnel  is  effected  either  by  a  covered  drain  under  the 
road-bed  at  the  centre  or  by  open  drains  at  the  sides. 

Artificial  ventilation  is  found  not  to  be  necessary  in  ordinary 
tunnels,  and  the  permanent  shafts  constructed  for  the  purpose 
have  been  considered  detrimental  rather  than  beneficial  in 
getting  rid  of  the  smoke.  The  passage  of  the  train  appears 
to  be  the  best  ventilator ;  the  air  being  thoroughly  disturbed 


450  CIVIL  ENGINEERING. 

and  displaced  by  the  quick  motion  of  the  train  through  the 
tunnel. 

623.  Ballast. — The  tops  of  the  embankments  and  the  bot- 
tom of  the  excavations  are  brought  to  a  height  called  the 
k<  formation  level,"  about  two  feet  below  the  intended  level  of 
the  rails.     The  remaining  two  feet,  more  or  less,  is  filled  up 
with  gravel,  or  gravel  and  sand,  or  broken  stone,  or  similar 
material,  througn  which  the  water  will  pass  freely.      This 
layer  is  called  the  "  ballast,"   and  the  material  of  which  it  is 
composed  should  be  clean  and  hard,  so  as  not  to  pack  into  a 
solid  mass  preventing  the  water  from  passing  through  it. 

The  object  of  the  ballast,  besides  allowing  the  water  to  run 
off  freely,  is  to  hold  the  Sleepers  firmly  in  their  places  and  to 
give  elasticity  to  the  road-bed. 

624.  Cross  ties. — The  cross  ties  or  "  sleepers  "  are  of  wood, 
hewn  flat  on  the  top  and  bottom  ;  they  are  from  7  to  9  feet 
long  for  the  ordinary  gauge,  6  inches  deep,  and  from  6  to  10 
inches  wide.     The  distance  between  the  ties  depends  upon 
the  weight  of  the  engines  used  on  the  road  and  the  strength 
of    the    rail;    2£   feet  from   centre  to  centre  is  about  the 
usual  distance.     The  nearer  the  sleepers  are  to  uniformity  in 
size  and  to  being  equidistant  from  each  other,  the  more  uni- 
form will  the  pressure  from   the    passage   of  the  train  be 
distributed  over  the  ground. 

The  sleepers  may  be  of  oak,  pine,  locust,  hemlock,  chest- 
nut, etc.  They  last  from  5  to  10  years,  depending  upon  their 
positions  and  the  amount  of  travel  over  them.  Their  duration 
may  be  increased  by  using  some  of  the  preservative  means 
referred  to  in  Art.  25. 

625.  Rails. — The  rails  are  made  of  wrought  iron,  or  of 
wrought  iron  with  a  thin  bar  of  steel  forming  the  top  surface, 
or  entirely  of  steel. 

Since  the  rail  acts  as  a  support  for  the 
train  between  the  ties,  and  as  a  lateral 
guide    for   the    wheels,  it    must    possess 
strength  and  stiffness  to  a  marked  degree. 
The  top   surface   should  be  of  sufficient 
size  and  hardness  to  withstand  the  action 
of  the  rolling  loads,  and  the  bottom  surface 
should  be  wide  enough  to  afford  a  good 
_     bearing   upon   the   tie.      The  rail  should 
FIG.  230.  have  that  form  which  gives  the  required 

strength  with  the  least  amount  of  mate- 
rial. The  form  of  cross-section  in  most  general  use  at  the 
present  time  in  the  United  States  is  shown  in  Fig.  230.  This 
particular  rail  is  4^  inches  high  and  4  inches  wide  at  the 


ELEVATION   OF  .THE   OUTEK   BAIL. 

bottom.  The  width  of  the  head  varies  from  2J  to  2J  indies 
the  top  surface  having  a  convex  form,  circular  in  cross-section, 
described  with  a  radius  double  the  height  of  the  rail.  The 
thickness  of  the  rib  or  stem  is  generally  from  -J  to  f  of  an 
inch,  although  recent  experiments  would  indicate  that  a  less 
thickness  might  be  used  with  safety. 

The  rails  are  rolled  in  lengths  varying  from  15  to  21  feet, 
and  when  laid  are  connected  by  fish-joints  and  fastened  to 
the  cross-ties  by  spikes.  The  method  of  fastening  formerly 
used  was  to  confine  the  ends  of  the  rails  in  a  cast-iron  chair 
which  rested  on  the  cross-ties.  This  method  may  be  seen  on 
some  of  the  older  railroads,  but  is  fast  going  out  of  use  on 
all  first-class  roads. 

626.  Coning  of  the  'wheels.  —  The  wheel  running  on  the 
outer  rail  of  a  curve  has  to  pass  over  a  greater  distance  than 
the  one  running  on  the  inner  rail.     Since  the  wheels  and  axles 
are  firmly  connected,  some  arrangement  must  be  made  to  keep 
the  wheels  from  dragging  or  slipping  on  the  rails  and  to  re- 
duce the  twisting  strain  brought  on  the  axles.     This  is  usually 
effected  by  making  the  tread  of  the  wheel  conical  instead  of 
cylindrical,  so  that  the  tendency  of  the  car  to  press  against 
the  outer  rail  brings  a  larger  diameter  upon  the  outer  and  a 
smaller  diameter  on  the  inner  rail.     The  difference  between 
these  diameters  must  be  proportioned  to  the  distance  to  be 
traversed  by  the  wheels,  and  must  depend,  therefore,  upon 
the  radius  of  the  curve  and  the  gauge.     The  sharper  the  curve, 
the  greater  should  be  the  difference  between  the  diameters. 
Upon  many  roads  it  is  customary  to  widen  the  gauge  from  4 
feet  8J  inches  to  4  feet  9  inches  on  sharp  curves,  thus  allowing 
more  play  for  the  wheels  and  giving  a  greater  difference  in  the 
diameters  of  those  parts  of  the  wheel  in  contact  with  the  rails. 
As  the  tread  of  the  wheel  is  conical,  the  tops  of  the  rails 
are  inclined,  or  given  a  "  cant  n  to  fit  this  cone.     The  amount 
of  inclination  depends  upon  the  amount  of  conical  form  given 
to  the  tread  of  the  wheel.    For  the  common  gauge,  this  inclina- 
tion is  taken  at  about  -fa. 

627.  Elevation  of  the  outer  rail.  —  When   the   track   is 
straight,  a  line  drawn  in  the  cross-section  made  by  a  plane 
perpendicular  to  the  axis  of  the  road,  tangent  to  the  upper 
surfaces  of  the  rails,  is  horizontal.     On  the  curved  portions 
of   the  track  the  centrifugal  force  tends  to  throw  the  car 
against  the  outer  rail.     This  tendency  is  resisted  by  raising 
the  outer  rail  to  a  certain  height  above  the  inner  one.    The  rule 
for  obtaining  this  height  is  expressed  as  follows  : 


(176) 


459 


CIVIL  ENGINEERING. 


in  which  h  is  the  elevation  above  inner  rail  in  inches ;  v,  the 
velocity  in  feet  per  second;  g,  the  gauge  of  the  road  in 
inches ;  and  R,  the  radius  of  the  curve  in  feet. 

628.  Crossings,  switches,  etc. — To  enable  trains  to  pasa 
from  one  track  to  the  other,  crossings  are  arranged  as  shown 
in  Fig.  231.  The  connection  between  the  crossing  and  the 
track  is  made  by  a  switch. 


FIG.  231. 


The  switch  consists  of  one  length  of  rails,  movable  around 
one  of  the  ends,  so  that  the  other  can  be  displaced  from  the 
line  of  the  main  track  and  joined  with  that  of  the  crossing,  or 
the  reverse,  depending  upon  which  line  of  rails  the  train  is  to 
use.  A  vertical  lever  is  attached  to  the  movable  end  by 
means  of  which  the  ends  of  the  rails  are  pushed  forward  or 
shoved  back,  making  the  connection  with  the  tracks.  The 
handles  of  the  lever  should  be  so  fashioned  and  painted  that 
their  position  may  be  seen  from  a  considerable  distance. 

Where  one  line  of  rails  crosses  another,  an  arrangement 
called  a  crossing-plate,  or  frog  (Fig.  232),  is  used  to  allow 
free  passage  of  the  wheels. 


PIG.  232. 

In  order  that  the  wheels  should  run  smoothly  on  the  rail 
A  B,  the  rail  C  D  must  be  cut  at  its  intersection  with  the 
former ;  for  a  similar  reason,  the  rail  A  B  must  be  cut  at  ita 
intersection  with  C  D. 

A  guard-rail,  G  G,  is  used  to  confine  the  opposite  wheel  for 
short  distance  and  prevent  the  wheel  running  on  A  B  from 
leaving  the  rail  at  the  cut.  This  guard-rail  is  parallel  to  th<? 


NAVIGABLE   CANALS.  453 

outer  rail  and  placed  about  two  inches  from  it.  It  extends 
a  short  distance  beyond  the  opening  in  both  directions  and 
has  its  ends  curved  slightly,  as  shown  in  Fig.  231. 

The  angle  between  the  lines  of  the  main  track  and  the 
crossing  should  be  very  small,  not  greater  than  3°. 

629.  Turn-tables. — When  the  angle  is  too  great  to  use  the 
crossing,  the  arrangement  called   a  turn-table  is  employed. 
This  cousists  of  a  strong  circular  platform  of  wood  or  iron, 
movable  around  its  centfe  by  means  of  conical  rollers  beneath 
it  running  upon  iron  roller- ways.     Two  rails  are  laid  upon 
the  platfdrm  to  receive  the  car,  which  is  transferred  from  one 
track  to  the  other  by  turning  the  platform  sufficiently  to  place 
the  rails  upon  it  in  the  same  line  with  those  of  the  track  upon 
which  the  car  is  to  run.     The  greater  the  proportion  of  the 
weight  borne  by  the  pivot  at  the  centre  and  the  less  that 
borne  by  the  rollers,  the  less  will  be  the  friction. 

630.  Telegraph,  mile-posts,  etc. — On  all  well  managed 
railroads,  telegraph  lines  are  essential  to  the  safe  working  of 
the  road.     These  should  be  connected  with  every  station.     By 
their  use,  the  positions  of  the  different  trains  at  all  hours  are 
made  known. 

Mile-posts,  numbered  in  both  directions,  should  be  placed 
along  the  sides  of  the  road.  Posts  showing  the  grades,  the 
distance  to  crossings  of  roads,  to  bridges,  etc.,  should  be  used 
wherever  necessary. 


CHAPTER  XXIV. 

CANALS. 

631.  A  canal  is  an  artificial  water-course.      Canals   are 
used  principally  for  purposes  of  inland  navigation ;  for  irriga- 
tion;   for  drainage;    for  supplying  cities  and  towns  with 
water,  etc. 

NAVIGABLE   CANALS. 

632.  Navigable  canals  may  be  divided  into  three  classes ; 
level  canals,  or  those  which  are  on  the  same  level  through- 
out ;  lateral  canals,  or  those  which  connect  two  points  of 
different  levels,  but  have  no  summit  level ;  and  canals  -with 
a  summit  level,  or  those  connecting  two  points  which  lie 
on  opposite  sides  of  a  dividing  ridge. 


4:54  CIVIL   ENGINEERING. 

I.  Level  canals. — In  canals  of  this  class,  the  level  of  the 
water  is  the  same  throughout.     As  in  roads,  straightness  of 
direction  gives  way  to  economy  of  construction,  and  the  econ- 
omical   course  will    be  that  which  follows  a  contour  line, 
unless  a  great  saving  may  be  made  by  using  excavation  or 
embankment.       Where  changes  of  direction  are   made,  the 
straight  portions  are  connected  by  curved  ones,  generally  arcs 
of  circles,  of  sufficient  curvature  to  allow  the  boats  using  the 
canal  to  pass  each  other  without  sensible  diminution  in  their 
rate  of  speed. 

II.  Lateral  canals. — In  these  canals,  the  fall  of  water  is  in 
one  direction  only.     Where  the  difference  of  level  between  the 
extreme  points  is  considerable,   the  canal  is  divided  injto  a 
series  of  levels  or  ponds,  connected  by  sudden  changes   of 
level.     These  sudden  changes  in  level  are  overcome  by  means 
of  locks  or  other  contrivances  by  which  the  boat  is  transferred 
from  one  level  to  the  other. 

III.  Canals  with  summit  levels. — These  are  canals  in 
which  the  points  connected  are  lower  than  the  intermediate 
ground  over  which  the  canal  has  to  pass,  and  in  consequence 
the  fall  is  in  both  directions.     As  the  water  for  the  supply  of 
the  summit  level  must  be  collected  from  the  ground  which 
lies  above  it,  it  follows  that  the  summit  level  should  be  at  the 
lowest  point  of  the  ridge  dividing  the  two  extremes  of  the 
canal. 

633.  Form  and  dimensions  of  water-way. — The  general 
width  of  a  canal  should  be  sufficient  to  allow  two  boats  to 
pass  each  other  easily.  Where  great  expense  would  be  in- 
curred in  giving  this  width,  like  that  of  a  bridge  supporting  a 
canal,  short  portions  may  be  made  just  wide  enough  for  one 
boat. 

The  depth  should  be  such  as  not  to  materially  increase  the 
resistance  to  the  motion  of  the  boat  beyond  what  is  felt  in 
open  water.  , 

The  bottom  of  the  canal  is  generally  made  horizontal.  The 
sides  are  inclined,  and  when  of  earth  should  not  be  steeper 
than  one  upon  one  and  a  half ;  if  of  masonry,  the  sides  may 
be  vertical  or  nearly  so.  In  the  latter  case  a  greater  width 
must  be  given  to  the  bottom  of  the  canal. 

The  water-way  is  usually  of  a  trapezoidal  form,  in  cross- 
section  (Fig.  233)  with  an  embankment  on  each  side,  raised 
above  the  general  surface  of  the  country  and  formed  of  the 
material  from  the  excavation  for  the  canal. 

The  relative  dimensions  of  the  parts  of  the  cross-section 
may  be  generally  stated  as  follows : 


TOWPATH.  455 

The  width  of  the  water-way,  at  bottom,  should  ue  at  least 
twice  the  width  of  the  boats  used  in  navigating  the  canal. 

The  depth  of  the  water-way  should  be  at  least  eighteen 
inches  greater  than  the  greatest  draft  of  the  boat. 


FIG.  233.— A,  water- way.      B,  towpath.      C,  berm.      D,  Hide-drain.      E, 
puddling  of  clay. 

The  least  area  of  water-way  should  be  at  least  six  times  the 
greatest  midship  section  of  the  boat. 

634.  A  towpath  for  horses  is  made  on  one  of  the  em- 
bankments and  a  footpath  on  the  other.     This  footpath  should 
be  wide  enough  to  serve  as  an  occasional  towpath. 

The  towpath  should  be  from  ten  to  twelve  feet  wide,  to 
allow  the  horses  to  pass  each  other  with  ease ;  and  the  foot- 
path at  least  six  feet  wide.  The  height  of  the  surfaces  of 
these  paths,  above  the  water  surface,  should  not  be  less  than 
two  feet,  to  avoid  the  wash  of  the  ripple ;  nor  greater  than 
four  feet  and  a  half,  for  the  facility  of  the  draft  of  the 
horses  in  towing.  The  surface  of  the  towpath  should  incline 
slightly  outward,  both  to  convey  off  the  surface  water  in  wet 
weather  and  to  give  a  firmer  footing  to  the  horses,  which 
naturally  draw  from  the  canal. 

The  width  given  to  these  paths  will  give  a  sufficient  thick- 
ness to  the  embankments  to  resist  the  pressure  of  the  water 
against  them,  and  to  prevent  filtration  through  them,  provided 
the  earth  is  at  all  binding  in  its  composition. 

635.  Construction.  —  All  canal  embankments  should  be 
carefully  constructed.     The  earth  of  which  they  are  formed 
should  be  of  a  good  binding  character,  and  perfectly  free 
from    mould    and    all   vegetable    matter,   as    the   roots  of 
plants,  etc.     In  forming  the  embankments,  the  mould  should 
first  be  removed   from  the  surface  on  which   they  are  to 
rest,   and  the  earth   then   spread   in   uniform  layers,   from 
nine  to  twelve  inches  thick,  and  well  rammed.     If  the  char- 
acter of  the  earth,  of  which  the  embankments  are  formed,  is 
such  as  not  to  present  entire  security  against  filtration,  a  pud- 
dling of  clay,  two  or  three  feet  thick,  should  be  laid  in  the 
interior  of  the  mass,  extending  from  about  a  foot  below  the 
natural  surface  up  to  the  same  level  with  the  surface  of  the 
water.     Sand  is  useful  in  stopping  leakage  through  the  holes 


456 


CIVIL  ENGINEERING. 


made  in  the  embankments  near  the  water  surface  by  insects, 
moles,  rats,  etc. 

The  side  slopes  of  the  embankment  vary  with  the  character 
of  the  soil :  towards  the  water-way  they  should  seldom  be  less 
than  two  base  to  one  perpendicular ;  from  it,  they  may  be 
less.  The  interior  slope  is  usually  not  carried  up  unbroken 
from  the  bottom  to  the  top ;  but  a  horizontal  space,  termed  & 
bench  or  berm,  about  one  or  two  feet  wide,  is  left,  about  one 
foot  above  the  water  surface,  between  the  side  slope  of  the 
water-way  and  the  foot  of  the  embankment  above  the  berm. 
This  space  serves  to  protect  the  upper  part  of  the  interior 
side  slope,  and  is,  in  some  cases,  planted  with  such  shrubbery 
as  grows  most  luxuriantly  in  moist  localities,  to  protect  more 
efficaciously  the  banks  by  the  support  which  its  roots  give  to 
the  soil.  The  side  slopes  are  better  protected  by  a  revetment 
of  dry  stone,  from  six  to  nine  inches  thick.  Aquatic  plants 
of  the  bulrush  kind  have  been  used,  with  success,  for  the 
same  purpose ;  being  planted  on  the  bottom,  at  the  foot  of 
the  side  slope,  they  serve  to  break  the  ripple,  and  preserve 
the  slopes  from  its  effects. 

Side  drains  must  be  made,  on  each  side,  a  foot  or  two  from 
the  embankments,  to  prevent  the  surface  water  of  the  natural 
surface  from  injuring  the  embankments. 

636.  Slight  leakage  may  sometimes  be  stopped  by  sprinkling 
fine  sand  in  small  quantities  at  a  time  over  the  surface  of  the 


water  in  the  vicinity  of  the  leaks.  The  sand  settling  to  the 
bottom  gradually  fills  the  crevices  in  the  sides  and  bottom  of 
the  canal  through  which  the  water  escapes* 

The  leakage  may  be  so  great  that  it  may  be  necessary,  in 
certain  cases,  to  line  the  canal  with  masonry,  concrete,  or  to 
face  the  sides  with  sheet-  piling  to  retain  the  water. 

When  the  bottom  of  the  canal  is  composed  of  fragments 
of  rock  forming  large  crevices,  or  composed  of  marl,  it  ha8 
been  frequently  found  necessary  to  line  the  water-way  in  such 
localities  with  masonry  (Fig.  234)  or  with  concrete. 


LOCKS. 


457 


In  a  lining  of  this  kind,  the  stone  used  was  about  four 
inches  thick,  laid  in  cement  or  hydraulic  mortar,  and  covered 
with  a  coating  of  mortar  two  inches  thick,  making  the  entire 
thickness  of  the  lining  six  inches.  This  lining  was  then  covered, 
both  at  bottom  and  on  the  sides,  by  a  layer  of  earth,  at  least 
three  feet  thick,  to  protect  it  from  the  shock  of  the  boats  strik- 
ing against  it. 

637.  Size  of  canals. — The  size  of  a  canal  depends  upon  the 
size  of  the  boats  to  be  used  upon  it.     The  dimensions  of  com- 
mon canal  boats  have  been  fixed  with  a  view  of  horses  being 
used  to  draw  them.     The  most  economical  use  of  horse-power 
is  to  draw  a  heavy  load  at  a  low  rate  of  speed.     Assuming  a 
speed  of  from  two  to  two  ^nd  a  half  miles  an  hour,  a  horse 
can  draw  a  boat  with  its  load,  in  all  about  170  tons.     This 
requires  a  boat  of  the  ordinary  cross-section  to  be  about  twelve 
feet  wide,  and  to  have  a  draught  of  four  and  a  half  feet  when 
fully  loaded. 

Boats  of  greater  cross-section  are  frequently  used,  and  are 
drawn  by  various  applications  of  steam  as  well  as  by  horse- 
power. The  methods  used  are  various,  as  the  screw  propeller, 
stationary  engines  with  endless  wire  ropes,  etc.  Canals  are 
sometimes  made  only  twelve  feet  wide  at  bottom,  with  a 
draught  of  four  feet ;  common  canals  are  from  twenty-five  to 
thirty  feet  wide  at  bottom,  with  a  depth  of  from  five  to  eight 
feet ;  ship  or  large  canals  are  fifty  feet  wide  at  bottom,  and 
have  a  depth  of  twenty  feet.  These  are  the  minimum  dimen- 
sions. 

638.  Locks. — An  arrangement  termed  a  lock  is  ordinarily 
used  to  pass  a  boat  from  one  level  to  another. 

A  lock  is  a  small  basin  just  large  enough  to  receive  a  boat, 
and  in  which  the  water  is  usually  confined  on  the  sides  by 


FIG.  235. 

two  upright  walls  of  masonry,  and  at  the  ends  by  two 
gates ;  the  gates  open  and  shut,  both  in  order  to  allow  the 
passage  of  the  boat  and  to  cut  off  the  water  of  the  upper  level 
from  the  lower,  or  from  the  water  in  the  lock. 

A  lock  (Figs.  235  and  236)  may  be  divided  into  three  dis- 
tinct parts :    1st.  The  part  included  between  the  two  gates, 


1:58  CIVIL  ENGINEERING. 

which  is  termed  the  chamber.  2d.  The  part  above  the 
upper  gates,  termed  the  fore  or  head-bay.  3d.  The  part 
below  the  lower  gates,  termed  the  aft  or  tail-bay. 

Fig.  235  shows  a  vertical  longitudinal  section  through  the 
axis  of  a  single  lock  built  on  a  foundation  of  concrete,  and 
Fig.  236  represents  the  plan. 


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tr 

13 

FIG.  236. 

In  these  figures,  A  is  the  lock-chamber ;  E,  E,  the  side 
walls ;  B,  the  head-bay ;  C,  the  tail-bay  ;  and  D,  the  lift-wall. 

The  lock-chamber  must  be  wide  enough  to  allow  an  easy 
ingress  and  egress  to  the  boats  commonly  used  on  the  canal ; 
a  breadth  of  one  foot  greater  than  the  greatest  breadth  of 
the  boat  is  deemed  sufficient  for  this  purpose.  The  length 
of  the  chamber  is  regulated  by  that  of  the  boats ;  it  should 
be  such  that  when  the  boat  enters  the  lock  from  the  lower 
level,  the  tail-gates  may  be  shut  without  requiring  the  boat 
to  unship  its  rudder. 

The  plan  of  the  chamber  is  usually  rectangular,  the  sides 
receiving  a  slight  batter ;  as  when  so  arranged  they  are  found 
to  give  greater  facility  to  the  passage  of  the  boat  than  when 
vertical.  The  bottom  of  the  chamber  is  either  flat  or  curved  ; 
more  water  will  be  required  to  fill  the  flat-bottomed  chamber 
than  the  curved,  but  less  masonry  will  be  required  in  its  con- 
struction. 

The  chamber  is  terminated  just  within  the  head-gates  by 
a  vertical  wall,  the  plan  of  which  is  usually  curved.  As  this 
wall  separates  the  upper  from  the  lower  level,  it  is  termed 
the  lift-wall ;  it  is  usually  of  the  same  height  as  the  lift  of 
the  levels.  The  top  of  the  lift- wall  is  formed  of  cut  stone, 
the  vertical  joints  of  which  are  normal  to  the  curved  face  of 
the  wall;  this  top  course  projects  from  six  to  nine  inches 
above  the  bottom  of  the  upper  level,  presenting  an  angular 
point  for  the  bottom  of  the  head-gates,  when  shut,  to  rest 
against.  This  projection  is  termed  the  mitre -sill.  Various 
degrees  of  opening  have  been  given  to  the  angle  between  the 
two  branches  of  the  mitre-sill;  it  is,  however,  generally  so 


LOOKS.  459 

determined,  that  the  perpendicular  of  the  isosceles  triangle, 
formed  by  the  two  branches,  shall  vary  between  one- fifth  and 
one-sixth  of  the  base. 

The  side-walls  sustain  the  pressure  of  the  embankment 
against  them,  and  when  the  lock  is  full  the  pressure  from  the 
water  in  the  chamber.  The  former  pressure  is  the  greater 
and  the  more  permanent  of  the  two  and  the  dimensions  of  the 
wall  are  determined  to  resist  this  pressure.  The  usual  man- 
ner of  doing  this  is  to  make  the  wall  four  feet  thick  at  the 
water  line  of  the  upper  level,  to  secure  it  against  filtration ; 
and  then  to  determine  the  base  of  the  batter,  so  that  the  mass 
of  masonry  shall  present  sufiicient  stability  to  resist  the  thrust 
of  the  embankment.  The  spread  and  other  dimensions  of 
the  foundations  will  be  regulated  according  to  the  nature  of 
the  soil,  as  in  other  masonry  structures. 

The  bottom  of  the  chamber,  as  has  been  stated,  may  be 
either  flat  or  curved.  The  flat  bottom  is  suitable  to  firm 
soils,  which  will  neither  yield  to  the  vertical  pressure  of  the 
chamber  walls  nor  admit  the  water  to  filter  from  the  upper 
level  under  the  bottom  of  the  lock.  In  either  of  these  cases, 
where  yielding  or  undermining  may  be  expected,  the  bottom 
should  be  an  inverted  arch.  The  thickness  of  the  masonry 
of  the  bottom  will  depend  on  the  width  of  the  chamber  and 
the  nature  of  the  soil.  Were  the  soil  a  solid  rock,  no  bottom- 
ing would  be  requisite ;  if  it  is  of  soft  material,  a  very  solid 
bottoming,  from  three  to  six  feet  in  thickness,  may  be  neces- 
sary. Great  care  must  be  taken  to  prevent  the  water  from 
the  upper  level  filtering  through  and  getting  under  the  bot- 
tom of  the  lock. 

The  lift-wall  may  have  only  the  same  thickness  as  the  side' 
walls,  but  unless  the  soil  is  very  firm,  it  would  be  more  pru- 
dent to  form  a  general  mass  of  masonry  under  the  entire 
head-bay,  to  a  level  with  the  base  of  the  chamber  founda- 
tions, of  which  mass  the  lift-wall  should  form  a  part. 

The  head-bay  is  enclosed  between  two  parallel  walls,  which 
form  a  part  of  the  side  walls  of  the  lock.  They  are  termi- 
nated by  two  wing  walls,  m,  m,  at  right  angles  with  the  side 
walls.  A  recess,  termed  the  gate-chamber,  is  made  in  the 
wall  of  the  head-bay ;  the  depth  of  this  recess  should  be  suf- 
ficient to  allow  the  gate,  when  open,  to  fall  two  or  three 
inches  within  the  facing  of  the  wall,  so  that  it  may  be  out  of 
the  way  when  a  boat  is  passing;  the  length  of  the  recess 
should  "be  greater  than  the  width  of  the  gate.  That  part  of 
the  recess  where  the  gate  turns  on  its  pivot  is  termed  the 
hollow  quoin ;  it  receives  what  is  termed  the  heel  or  quoin- 
post  of  the  gate,  which  is  made  to  fit  the  hollow  quoin.  The 


460  CIVIL   ENGINEERING. 

distance  between  the  hollow  quoins  and  the  face  of  the  lift- 
wall  will  depend  on  the  pressure  against  the  mitre-sill,  and 
the  strength  of  the  stone ;  eighteen  inches  will  generally  be 
found  sufficient. 

The  side  walls  need  not  to  extend  more  than  twelve  inches 
beyond  the  other  end  of  the  gate-chamber.  The  wing  walls 
may  be  extended  back  to  the  total  width  of  the  canal,  but  it 
will  be  more  economical  to  narrow  the  canal  near  the  lock, 
and  to  extend  the  wing  walls  only  about  two  feet  into  the 
banks  or  sides.  The  dimensions  of  the  side  and  wing  walla 
of  the  head-bay  are  regulated  in  the  same  way  as  the  chamber 
walls.  The  top  of  the  side  walls  of  the  lock  may  be  from 
one  to  two  feet  above  the  general  level  of  the  water  in  the 
upper  level. 

The  bottom  of  the  head-bay  is  flat,  and  on  the  same  level 
with  the  bottom  of  the  canal ;  the  exterior  course  of  stones  at 
the  entrance  to  the  lock  should  be  so  jointed  as  not  to  work 
loose. 

The  side  walls  of  the  tail-bay  are  also  a  part  of  the  general 
side  walls,  and  their  thickness  is  regulated  as  in  the  preceding 
cases.  Their  length  will  depend  chiefly  on  the  pressure  which 
the  lower  gates  throw  against  them  when  the  lock  is  full,  and 
partly  on  the  space  required  by  the  lockmen  in  opening  and 
shutting  the  gates.  These  walls  are  also  terminated  by  wing 
walls,  n,  n,  similarly  arranged  to  those  of  the  head-bay.  The 
points  of  junction  between  the  wing  and  side  walls  should,  in 
both  cases,  either  be  curved  or  the  stones  at  the  angles  be 
rounded  off .  One  or  two  perpendicular  grooves  are  sometimes 
made  in  the  side  walls  of  the  tail-bay,  to  receive  stop-planks, 
when  a  temporary  dam  is  needed,  to  shut  off  the  water  of  the 
lower  level  from  the  chamber,  in  case  of  repairs,  etc. 

The  gate-chambers  for  the  lower  gates  are  made  in  the 
chamber  walls ;  the  bottom  of  the  chamber,  where  the  gates 
swing  back,  should  be  flat,  or  be  otherwise  arranged  so  as 
not  to  impede  the  play  of  the  gates. 

The  bottom  of  the  tail-bay  is  arranged,  in  all  respects,  like 
that  of  the  head-bay. 

639.  Those  parts  of  the  lock  where  there  is  great  wear  and 
tear,  as  at  the  angles  generally,  should  be  of  cut-stone ;  or 
where  an  accurate  finish,  is  indispensable,  as  at  the  hollow 
quoins.  The  other  parts  may  be  of  brick,  rubble,  concrete, 
etc.,  but  every  part  should  be  laid  in  cement  or  the  best 
hydraulic  mortar. 

The  mitre-sills  are  generally  faced  with  timber,  to  enable 
them  to  withstand  better  the  blows  which  they  receive  from 
the  gates,  and  to  make  a  tighter  joint. 


LOOK   GATES.  461 

640.  The  locks  are  filled  and  emptied  through  sluices  in 
the  head  and  tail-gates,  opened  and  closed  by  slide  valves,  rr 
by  culverts  made  of  masonry  or  iron  pipe  placed  as  shown 
in  the  figures  at  c,  c,  c,  etc.     The  latter  is  the  method  gene- 
rally recommended.     From  the  difficulty  of  repairing  the 
sluices  when  out  of  order,  many  prefer  the  use  of  valves  in 
the  gates. 

The  bottom  of  the  canal  below  the  lock  should  be  protected 
by  what  is  termed  an  apron,  which  is  a  covering  of  plank 
laid  on  a  grillage,  or  of  dry  stone.  The  length  will  depend 
upon  the  strength  of  the  current ;  generally  a  distance  of 
from  fifteen  to  thirty  feet  will  be  sufficient. 

641.  Lock  gates. — The  gates  may  be  made  of  wood  or  of 
iron.     Each  gate  is  ordinarily  composed  of  two  leaves,  each 
leaf  consisting  of  a  framework,  covered  with  planking  or  iron 
plates.     The  frame,  when  of  timber,  consists  usually  of  two 
uprights,  connected  by.horizontal  pieces  let  into  the  uprights 
with  the  usual  diagonal  bracing. 

In  gates  of  this  kind,  each  leaf  turns  about  an  upright, 
which  is  called  the  quoin  or  heel-post.  This  post  is  cylin- 
drical on  the  side  next  to  the  hollow  quoins,  which  it  exactly 
fits  when  the  gate  is  shut.  It  is  made  slightly  eccentric,  so 
that  when  the  gate  is  opened  it  may  turn  easily  without  rub- 
bing against  the  quoin.  At  its  lower  end  it  rests  on  a  pivot, 
and  its  upper  end  turns  in  a  circular  collar  which  is  strongly 
anchored  in  the  masonry  of  the  side  walls.  One  of  the 
anchor-irons  is  usually  placed  in  a  line  with  the  leaf  when 
shut,  the  other  in  a  line  with  it  when  open ;  these  being  the 
best  positions  to  resist  most  effectually  the  strain  produced 
by  the  gate.  The  opposite  upright,  termed  the  mitre-post, 
has  one  edge  bevelled  off,  to  tit  against  the  mitre-post  of  the 
other  leaf  of  the  gate,  forming  a  tight  joint  when  the  gate  is 
shut. 

A  long,  heavy  beam,  termed  a  balance  beam  from  its 
partially  balancing  the  weight  of  the  leaf,  is  framed  upon  the 
quoin-post,  and  is  mortised  into  the  mitre-post.  The  balance 
beam  should  be  abou-t  four  feet  above  the  top  of  the  lock ;  its 
principal  use  being  to  bring  the  centre  of  gravity  of  the  leaf 
near  the  heel-post  and  to  act  as  a  lever  to  open  and  shut  the 
leaf. 

Sometimes  this  bar  is  dispensed  with,  and  the  leaves  are 
supported  on  rollers  placed  under  the  lower  side  to  assist  the 
pivot  in  supporting  their  weight.  These  rollers  run  on  iron 
rails  placed  on  the  floor  of  the  gate-chamber.  In  these  cases 
the  gates  are  ordinarily  opened  and  shut  by  means  of  wind- 
lasses and  chains.  This  is  the  method  generally  used  for 


462  CIVIL  ENGINEERING. 

very  large  gates.     Gates  formed  of  a  single  leaf  moving  on  a 
horizontal  axis  are  frequently  used. 

642.  Inclined  planes. — Instead  of  locks,  inclined  planes 
are  sometimes  used,  by  means  of  which  the  boats  are  passed 
from  one  level  to  another.     In  these  cases,  water-tight  cais- 
sons or  cradles,  on  wheels  are  used. 

At  the  places  where  the  levels  are  to  be  connected,  the 
canal  is  deepened  to  admit  of  the  caisson  or  the  cradle  to  run 
in  under  the  boat  to  be  transferred.  Two  parallel  lines  of 
rails  start  from  the  bottom  of  the  lower  level,  ascend  an  in- 
clined plane  up  to  a  summit  a  little  above  the  upper  level, 
and  then  descend  by  a  short  inclined  plane  into  the  upper 
level.  Two  caissons  or  cradles,  one  on  each  set  of  rails,  are 
connected  by  a  wire  rope,  so  that  one  ascends  while  the  other 
descends.  Power  being  applied,  the  boats  are  transferred  to 
the  appropriate  levels. 

The  caissons  are  preferred  because  they  balance  each  other 
at  all  times  on  the  inclined  plane,  whether  the  boats  are  light 
or  heavy,  as  they  displace  exactly  their  own  weight  of  water 
in  the  caisson.  In  some  cases,  the  caissons  have  been  lifted 
vertically  instead  of  being  drawn  up  inclined  planes. 

643.  Guard   lock. — A  large   basin  is  usually  formed   at 
the  outlet,  for  the  convenience  of  commerce ;  and  the  en- 
trance from  this  basin  to  the  canal,  or  from  the  river  to  the 
basin,  is  effected  by  means  of  a  lock  with  double  gates,  so 
arranged  that  a  boat  can  be  passed  either  way,  according  as 
the  level  in  the  one  is  higher  or  lower  than  that  in  the  other. 
A  lock  so  arranged  is  termed  a  tide  or  guard  lock,  from  its 
uses.     The  position  of  the  tail  of  this  lock  is  not  indifferent 
in  all  cases  where  it  forms  the  outlet  to  the  river ;  for  were 
the  tail  placed  up  stream,  it  would  generally  be  more  difficult 
to  pass  in  or  out  than  if  it  were  down  stream. 

644.  Lift  of  locks. — The  vertical  distance  through  which 
a  boat  is  raised  or  lowered  by  means  of  the  lock  is  called  the 
"  lift."      This  vertical  distance  between  two  levels  may  be 
overcome  by  the  use  of  a  single  lock  or  by  a  "  flight  of  locks." 
The  lift  of  a  single  lock  ranges  from  two  to  twelve  feet,  but 
generally  in  ordinary  canals  is  taken  at  about  eight  feet. 
Where  a  greater  distance  than  twelve  feet  has  to  be  over- 
come, two  or  more,  or  a  flight  of  locks,  are  necessary. 

In  fixing  the  lengths  of  the  levels  and  the  positions  of  the 
locks,  the  engineer,  if  considering  the  expenditure  of  water, 
will  prefer  single  locks  with  levels  between  them,  to  a  flight 
of  locks. 

In  most  cases,  a  flight  is  cheaper  than  the  same  number  of 
single  locks,  as  there  are  certain  parts  of  the  masonry  which 


WATER   SUPPLY.  463 

can  be  omitted.  There  is  also  an  economy  in  the  omission  of 
the  small  gates,  which  are  not  needed  in  flights.  It  is,  how- 
ever, more  difficult  with  combined  than  with  single  locks 
to  secure  the  foundations  from  the  effects  of  the  water,  which 
forces  its  way  from  the  upper  to  the  lower  level  under  the 
locks.  Where  an  active  trade  is  carried  on,  a  double  flight  is 
sometimes  arranged,  one  for  the  ascending,  the  other  for  the 
descending  boats.  In  this  case  the  water  which  fills  one  flight 
may,  after  the  passage  of  the  boat,  be  partly  used  for  the 
other,  by  an  arrangement  of  valves  made  in  the  side  wall 
separating  the  locks. 

The  engineer  is  not  always  left  free  to  select  between  the 
two ;  for  the  form  of  the  natural  surface  may  require  him  to 
adopt  a  flight  at  certain  points.  In  a  flight  the  lifts  are 
made  the  same  throughout,  but  in  single  locks  the  lifts  vary 
,  according  to  circumstances.  Locks  with  great  lifts  consume 
more  water,  require  more  care  in  their  construction,  and  re- 
quire greater  care  against  accidents  than  the  smaller  ones, 
but  cost  less  for  the  same  difference  of  level. 

645.  Levels. — The   position  and   the   dimensions  of  the 
levels  must  be  mainly  determined  by  the  form  of  the  natural 
surface.      By  a  suitable  modification  of   its  cross-section,  a 
level  can  be  made  as  short  as  may  be  deemed  desirable  ;  there 
being  but  one  point  to  be  attended  to  in  this,  which  is,  that  a 
boat  passing  between  the  two  locks,  at  the  ends  of  the  level, 
will  have  time  to  enter  either  lock  before  it  can  ground,  on 
the  supposition  that  the  water  drawn  off  to  fill  the  lower  lock, 
while  the  boat  is  traversing  the  level,  will  just  reduce  the 
depth  to  the  draught  of  the  boat. 

646.  Water  supply. — Two  questions  are  to  be  considered : 
the  quantity  of  water  required,  and  the  sources  of  supply. 

The  quantity  of  water  required  may  be  divided  into  two 
portions:  1st.  The  quantity  required  for  the  summit  level, 
and  those  levels  which  draw  from  it  their  supply.  2d.  The 
quantity  which  is  wanted  for  the  levels  below  those,  and 
which  is  furnished  from  other  sources. 

The  supply  of  the  first  portion,  which  must  be  collected  at 
the  summit  level,  may  be  divided  into  several  elements:  1st. 
The  quantity  required  to  fill  the  summit  level,  and  the  levels 
which  draw  their  supply  from  it.  2d.  The  quantity  required 
to  supply  losses,  arising  from  accidents ;  as  breaches  in  the 
banks  and  the  emptying  of  the  levels  for  repairs.  3d.  The 
supplies  for  losses  from  surface  evaporation,  from  leakage 
through  the  soil,  and  through  the  lock  gates.  4.  The  quan- 
tity required  for  the  service  of  the  navigation,  arising  from 
the  passage  of  the  boats  from  one  level  to  another. 


4:64:  OTVTL   ENGINEERING. 

The  quantity  required  to  fill  the  summit  level  and  its  de- 
pendent levels  will  depend  on  their  size,  an  element  which 
can  be  readily  calculated;  and  upon  the  quantity  which 
would  soak  into  the  soil,  which  is  an  element  of  a  very  inde- 
terminate character,  depending  on  the  nature  of  the  soil  in 
the  different  levels. 

The  supplies  for  accidental  losses  are  of  a  still  less  deter- 
minate character. 

The  supply  for  losses  from  surface  evaporation  may  be  de- 
termined by  observations  on  the  rain- fall  of  the  district,  and 
the  yearly  amount  of  evaporation.  Losses  caused  by  leakage 
through  the  soil  will  depend  on  the  greater  or  less  capacity 
which  the  soil  has  for  holding  water.  This  element  varies 
not  only  with  the  nature  of  the  soil,  but  also  with  the  shorter 
or  longer  time  that  the  canal  may  have  been  in  use ;  it  having 
been  found  to  decrease  with  time,  and  to  be,  comparatively, 
but  trifling  in  old  canals.  In  ordinary  soils  it  may  be  esti- 
mated at  about  two  inches  in  depth  every  twenty-four  hours,  for 
some  time  after  the  canal  is  first  opened.  The  leakage  through 
the  gates  will  depend  on  the  workmanship  of  these  parts. 

In  estimating  the  quantity  of  water  expended  for  the  ser- 
vice of  the  navigation,  in  passing  the  boats  from  one  level  to 
another,  two  distinct  cases  require  examination :  1st.  Where 
there  is  but  one  lock ;  and  2d.  Where  there  are  several  con- 
tiguous locks,  or,  as  it  is  termed,  a  flight  of  locks  between 
two  levels. 

To  pass  a  boat  from  one  level  to  the  other — from  the  lower 
to  the  upper  end,  for  example — the  lower  gates  are  opened, 
and  the  boat  having  entered  the  lock  they  are  shut,  and  water 
is  drawn  from  the  upper  level  to  fill  the  lock  and  raise  the 
boat ;  when  this  operation  is  finished,  the  upper  gates  are 
opened  and  the  boat  is  passed  out.  To  descend  from  the 
upper  level,  the  lock  is  first  filled ;  the  upper  gates  are  then 
opened  and  the  boat  passed  in ;  these  gates  are  next  shut,  and 
the  water  is  drawn  from  the  lock  until  the  boat  is  lowered  to 
the  lower  level,  when  the  lower  gates  are  opened  and  the  boat 
is  passed  out. 

Hence,  to  pass  a  boat,  up  or  down,  a  quantity  of  water 
must  be  drawn  from  the  upper  level  to  fill  the  lock  to  a  height 
which  is  equal  to  the  difference  of  level  between  the  surface 
of  the  water  in  the  two ;  this  volume  of  water  required  to 
pass  a  boat  up  or  down  is  termed  the  prism  of  lift.  The 
calculation,  therefore,  for  the  quantity  of  water  requisite  for 
the  service  of  the  navigation,  will  be  simply  that  of  the 
number  of  prisms  of  lift  which  each  boat  will  draw  from  the 
summit  level  in  passing  up  and  down. 


WATEB  SUPPLY.  465 

An  examination  of  the  quantity  of  water  used  in  passing 
from  one  level  to  another,  will  show  that  the  quantity  required 
for  a  flight  of  locks  is  greater  than  that  required  for  isolated 
locks. 

The  source  of  supply  of  water  is  the  rain-fall.  The  rain- 
water which  escapes  evaporation  on  the  surface  and  absorp- 
tion by  vegetable  growth,  either  runs  directly  from  the  surface 
of  the  ground  into  streams,  or  sinks  into  the  ground,  flows 
through  crevices  of  porous  strata  and  escapes  by  springs,  or 
collects  in  the  strata,  from  which  it  is  drawn  by  means  of  weUs. 

647.  In  whatever  way  the  water  may  be  collected,  the 
measurement  of  the  rain-fall  of  the  district  from  which  it 
comes  is  of  the  first  importance.  To  make  this  measurement, 
the  area  of  the  district  called  the  drainage  area  or  catchment 
basin,  and  the  depth  of  the  rain-fall  for  a  given  time  must  be 
determined. 

Drainage  area. — This  area  is  generally  a  district  of  country 
enclosed  by  a  ridge  or  water-shed  line  which  is  continuous 
except  at  the  place  where  the  waters  of  the  basin  find  an 
outlet.  It  may  be  divided  by  branch  ridges  or  spurs  into  a 
number  of  smaller  basins,  each  drained  by  a  stream  which 
runs  into  the  main  stream. 

Depth  of  rain-fall. — The  depth  is  determined  by  estab- 
lishing rain-gauges  in  the  district  and  having  careful  obser- 
vations made  for  as  long  a  period  as  possible. 

The  important  points  to  be  determined  are :  1.  The  least 
annual  rain-fall ;  2.  The-  mean  annual  rain-fall ;  3.  The  great- 
est annual  rain-fall ;  4.  The  distribution  of  the  rain-fall 
throughout  the  year ;  5.  The  greatest  continuous  rain-fall  in 
a  short  period. 

For  canal  purposes,  the  least  annual  rain-fall  and  the 
.ongest  drought  are  the  most  important  points  to  be  known. 

Knowing  the  depth  of  the  rain-fall  and  the  area  of  the 
catchment  basin,  an  estimate  of  the  amount  of  water  which 
may  be  available  for  the  canal  may  be  made.  Theoretically 
considered,  all  the  water  that  drains  from  the  ground  adjacent 
to  the  summit  level,  and  above  it,  might  be  collected  for  its 
supply ;  but  it  is  found  in  practice  that  channels  for  the  con- 
veyance of  water  must  have  certain  slopes,  and  that  these 
slopes,  moreover,  will  regulate  the  supply  furnished  in  a  cer- 
tain time,  all  other  things  being  equal.  The  actual  discharge 
of  the  streams  should  be  measured  so  as  to  find  the  actual 
proportion  of  available  to  total  rain-fall,  and  the  streams 
should  be  measured  at  the  same  time  the  rain-gauge  observa- 
tions are  made. 

The  measurement  of  the  quantity  of  water  discharged  bv  a 
30 


4:66  CIVIL   ENGINEERING. 

stream  is  called  "  gauging,"  and  to  be  of  value  should  Y.e  made 
with  accuracy  and  extend  through  some  considerable  time. 

648.  Feeders  an^  reservoirs. — The  usual  method  of  col- 
lecting the  water,  and  conveying  it  to  the  summit  level,  is 
by  feeders  and  reservoirs.     The  feeder  is  a  canal  of  a  small 
cross-section,  which  is  traced  on  the  surface  of  the  ground 
with  a  suitable  slope,  to  convey  the  water  either  into  the 
reservoir,  or  direct  to  the  summit  level.     The  dimensions  of 
the  cross-section,  and  the  longitudinal  slope  of  the  feeder, 
should  bear  certain  relations  to  each  other,  in  order  that  it 
shall  deliver  a  certain  supply  in  a  given  time.     The  smaller 
the  slope  given  to  the  feeder,  the  lower  will  be  the  points  at, 
which  it  will  intersect  the  sources  of  supply,  and  therefore 
the  greater  will  be  the  quantity  of  water  which  it  will  re- 
ceive.    The  minimum  slope,  however,  has  a  practical  limit, 
which  is  laid  down  at  four  inches  in  1,000  yards,  or  nine 
thousand  base  to  one  altitude  ;  and  the  maximum  slope  should 
not  be  so  great  as  to  give  the  current  a  velocity  which  would 
injure  the  bed  of  the  feeder.     Feeders  are  furnished,  like 
ordinary  canals,  with  contrivances  to  let  off  a  part,  or  the 
whole,  of  the  water  in  them,  in  cases  of  heavy  rains,  or  for 
making  repairs. 

A  reservoir  is  a  place  for  storing  water  to  be  held  in  re- 
serve for  the  necessary  supply  of  the  summit  level.  A  reser- 
voir is  usually  formed  by  choosing  a  suitable  site  in  a  deep 
and  narrow  valley,  which  lies  above  the  summit  level,  and 
erecting  a  dam  of  earth,  or  of  masonry,  across  the  outlet  of 
the  valley,  or  at  some  more  suitable  point,  to  confine  the  water 
to  be  collected.  The  object  to  be  obtained  is  to  collect  the 
greatest  volume  of  water,  and  at  the  same  time  present  the 
smallest  evaporating  surface,  at  the  smallest  cost  for  the  con- 
struction of  the  dam. 

649.  Darns. — The  dams  of  reservoirs  have  been  variously 
constructed :  in  some  cases  they  have  been  made  entirely  of 
earth ;  in  others,  entirely  of  masonry ;  and  in  others,  of  earth 
packed  in  between  parallel  stone  walls.     It  is  now  thought 
best  to  use  either  earth  or  masonry  alone,  according  to  the 
circumstances  of  the  case ;  the  comparative  expense  of  the 
two  methods  being  carefully  considered. 

Earthen  darns  should  be  made  with  extreme  care,  of  the 
best  binding  earth,  well  freed  from  everything  that  might 
cause  filtrations. 

The  foundation  is  prepared  by  stripping  off  the  soil  and 
excavating  and  removing  all  porous  materials,  such  as  sand, 
gravel,  and  fissured  rock,  until  a  compact  and  water-tight  bed 
is  reached. 


DAMS.  467 

A  culvert  for  the  outlet-pipes  is  next  built  This  should 
rest  on  a  foundation  of  concrete  and  should  have  the  masonry 
laid  in  cement  or  the  best  of  hydraulic  mortar.  It  should  be 
well  coated  with  a  clay  puddling.  Frequently  the  inner  end 
of  the  culvert  terminates  in  a  vertical  tower,  which  contains 
outlet-pipes  for  drawing  water  from  different  levels,  and  the 
necessary  mechanism  by  means  of  which  the  pipes  can  be 
closed  or  opened.  Sometimes  a  cast-iron  pipe  alone  is  laid 
without  any  culvert. 

The  earth  is  then  carefully  spread  in  layers  not  over  a  foot 
thick  and  rammed.  A  "  puddle-wall "  with  a  thickness  at  the 
base  of  about  one-third  its  height  and  diminishing  to  about 
half  this  thickness  at  the  top,  should  form  the  central  part  of 
the  dam.  Care  should  be  taken  that  it  forms  a  water-tight 
joint  with  the  foundation  and  also  with  the  puddle  coating 
of  the  culvert. 

The  dam  may  be  from  fifteen  to  twenty  feet  thick  at  top. 
The  slope  of  the  dam  towards  the  pond  should  be  from  three 
to  six  base  to  one  perpendicular ;  the  reverse  slope  need  only 
be  somewhat  less  than  the  natural  slope  of  the  earth. 

The  outer  slope  is  usually  protected  from  the  weather  by 
being  covered  with  sods  of  grass.  The  inner  slope  is  usually 
faced  with  dry  stone,  to  protect  the  dam  from  the  action  of 
the  surface  ripple. 


FIG.  237.— A,  body  of  the  dam. 

a,  top  of  the  waste -weir. 

6,  pool,  formed  by  a  stop-plank  dam  at  c,  to  break  the  fall  of  the 

water. 
d,  covering  of  loose  stone  to  break  the  fall  of  the  water  from  the 

pool  above. 

Masonry  dams  are  water-tigjht  walls,  of  suitable  forms 
and  dimensions  to  prevent  filtration,  and  to  resist  the  pressure 
of  water  in  the  reservoir.  The  cross-section  is  usually  that  of 
a  trapezoid,  the  face  towards  the  water  being  vertical,  and  the 
exterior  face  inclined  with  a  suitable  batter  to  give  the  wall 
sufficient  stability.  The  wall  should  be  at  least  four  feet  thick 


468  CIVIL  ENGINEERING. 

at  the  water  line,  to  prevent  filtration,  and  this  thickness  may 
be  increased  as  circumstances  may  require. 

650.  Waste-weirs. — Suitable  dispositions  should  be  made 
to  relieve  the  dam  from  all  surplus  water  during  wet  seasons. 
For  this  purpose  arrangements  should  be  made  for  cutting  off 
the  sources  of  supply  from  the  reservoir ;  and  a  cut,  termed  a 
waste-weir  (Fig.  237),  of  suitable  width  and  depth,  should 
be  made  at  some  point  along  the  top  of  the  dam,  and  be  faced 
with  stone,  or  wood,  to  give  an  outlet  to  the  water  over  the 
dam.     In  high  dams  the  total  fall  of  the  water  should  be 
divided  into  several  partial  falls,  by  dividing  the  exterior 
surface  over  which  the  water  runs  into  offsets.     To  break  the 
shock  of  the  water  upon  the  horizontal  surface  of  the  offset, 
it  should  be  covered  with  a  sheet  of  water  retained  by  a  dam 
placed  across  its  outlet. 

In  extensive  reservoirs,  in  which  a  large  surface  is  exposed 
to  the  action  of  the  winds,  waves  might  be  forced  over  the 
top  of  the  dam,  and  subject  it  to  danger;  in  such  cases  the 
precaution  should  be  taken  of  placing  a  parapet  wall  towards 
the  outer  edge  of  the  top  of  the  dam,  and  facing  the  top 
throughout  with  flat  stones  laid  in  mortar. 

651.  Water-courses  intersecting  the  line  of  the  canal. 
— The  disposition  of  the  natural  water-courses  %which  intersect 
the  line  of  the  canal  will  depend  on  their  size,  the  character 
of  their  current,  and  the  relative  positions  of  the  canal  and 
stream. 

Small  streams  which  lie  lower  than  the  canal  may  be  con- 
veyed under  it  through  an  ordinary  culvert.  If  the  level  of 
the  canal  and  stream  is  nearly  the  same,  it  may  be  conveyed 
under  the  canal  by  an  inverted  syphon  of  masonry  or  iron, 
usually  termed  a  broken-back  culvert,  or  if  the  water  of  the 
stream  is  limpid,  and  its  current  gentle,  it  may  be  received 
into  the  canal.  Its  communication  with  the  canal  should  be 
so  arranged  that  the  water  may  be  shut  off  or  let  in  at  plea- 
sure, in  any  quantity  desired. 

In  cases  where  the  line  of  the  canal  is  crossed  by  a  torrent, 
which  brings  down  a  large  quantity  of  sand,  pebbles,  etc.,  it 
may  be  necessary  to  make  a  permanent  structure  over  the 
canal,  forming  a  channel  for  the  torrent ;  but  if  the  discharge 
of  the  torrent  is  only  periodical,  a  movable  channel  may  be 
arranged,  for  the  same  purpose,  by  constructing  a  boat  with 
a  deck  and  sides  to  form  the  water-way  of  the  torrent.  The 
boat  is  kept  in  a  recess  in  the  canal  near  the  point  where  it 
is  used,  and  is  floated  to  its  position,  and  sunk  when  wanted. 

When  the  Aine  of  the  canal  is  intersected  by  a  wide  water- 
course, the  communication  between  the  two  shores  must  be 


IRRIGATING   CANALS.  469 

effected  either  by  a  canal  aqueduct  bridge,  or  by  the  boats 
descending  from  the  canal  into  the  stream. 

652.  Dimensions  of  canals  and  their  locks  in  the  United 
States. — The  original  dimensions  of  the  New  York  Erie  Canal 
and  its  locks  have  been  generally  adopted  for  similar  works 
subsequently  constructed  in  most  of  the  other  States.  The 
dimensions  of  this  canal  and  its  locks  were  as  follows :  . 

Width  of  canal  at  top 40  feet. 

Width  at  bottom 28     " 

Depth  of  water 4    " 

Width  of  tow-path 9  to  12     " 

Length  of  locks  between  mitre-sills 90    " 

Width  of  locks 15    « 

For  the  enlargement  of  the  Erie  Canal,  the  following  are 
the  dimensions : 

Width  of  canal  at  top 70  feet. 

Width  at  bottom 42     " 

Depth  of  water 7    " 

Width  of  tow-path ; 14    " 

Length  of  locks  between  mitre-sills 110     " 

Width  of  lock  at  top 18.8  " 

Width  of  lock  at  bottom 14.6  " 

Lift  of  locks 8    « 

Between  the  double  locks  a  culvert  is  placed,  which  allows 
the  water  to  now  from  the  level  above  the  lock  to  the  one 
below,  when  there  is  a  surplus  of  water  in  the  former. 


IBBIGATING   CANALS, 

653.  Canals  belonging  to  this  class  are  used  to  bring  from 
its  source  a  supply  of  water,  which,  when  reaching  certain 
localities,  is  made  to  flow  over  the  land  for  agricultural  pur- 
poses. This  kind  of  canal  is  practically  unknown  in  the 
United  States,  as  the  farmer  depends  almost  entirely  on  the 
rain-fall  alone  for  the  requisite  amount  of  moisture  for  his 
crops. 

Irrigation  canals  of  large  size  have  been  used  in  India  for 
hundreds  of  years ;  they  are  also  found  in  Italy.  Kude  imi- 
tations, of  small  size,  are  to  be  seen  in  Mexico,  the  territory 
of  New  Mexico,  lower  part  of  California,  and  other  parts  of 
the  United  States. 

In  certain  parts  of  our  country  they  could  be  used  to  great 


470  CIVIL   ENGINEERING. 

advantage,  and  since  in  the  future  they  may  be  used,  it  is 
thought  advisable  to  allude  briefly  to  them  in  this  treatise. 

The  special  difference  between  a  navigable  and  an  irri- 
gation canal  is  that  the  former  requires  that  there  should  be 
little  or  no  current  in  the  canal,  so  that  navigation  may  be 
easy  in  both  directions,  while  the  latter  requires  that  the 
canal  should  be  a  running  stream,  fed  by  continuous  supplies 
of  water  at  its  source,  to  make  up  the  losses  caused  by  the 
amounts  of  water  drawn  off  from  the  canal  for  the  purposes 
of  irrigation. 

Hence,  for  two  canals  of  the  same  size,  the  navigable 
canal  will  require  a  less  volume  of  water  than  the  irriga- 
tion canal,  and  is  more  economically  constructed  on  a  low 
level. 

The  irrigation  canal  should  be  carried  at  as  high  a  level  as 
possible,  so  as  to  have  sufficient  fall  for  the  water  which  is  to 
be  used  to  irrigate  the  land  on  both  sides  of  it  and  at  con- 
siderable distances  from  it.  This  irrigation  is  effected  by 
means  of  branch  canals  leading  from  the  main  one,  whence 
the  water  is  carried  by  small  channels  on  the  fields. 

654.  The  problem  of  an  irrigation  canal  is  to  so  connect  it 
with  the  stream  furnishing  the  supply  of  water,  and  to  so 
arrange  the  slope  of  the  bed  of  the  canal,  that  the  canal 
shall  not  become  choked  with  silt. 

A  canal  opening  direct  into  the  stream  which  supplies  it 
with  water,  if  proper  arrangements  are  not  made,  will  be  lia- 
ble to  have  the  volume  of  water  greatly  increased  in  time  of 
freshets,  and  at  other  times  have  the  supply  entirely  cut  off. 
In  the  first  case,  large  quantities  of  silt  would  be  washed  into 
the  canal,  choking  it  up  as  the  water  receded  to  its  proper 
level.  In  the  second  case,  the  supply  would  probably  fail  at 
the  critical  period  of  the  growing  crops  when  water  was 
greatly  needed. 

A  good  selection  of  the  point  where  the  canal  joins  the 
stream,  and  the  use  of  sluices  to  govern  the  supply  of 
water,  will  greatly  prevent  the  occurrence  of  either  of  these 
conditions. 

To  prevent  the  silting  up  of  the  canal,  the  slope  of  the  bed 
is  so  fixed  that  the  water  shall  have  a  uniform  velocity 
throughout.  It  is  therefore  seen  that,  as  the  water  is  drawn 
off  at  different  points  for  the  irrigation  of  the  land,  on  the 
right  and  left  of  the  canal,  the  volume  of  water  is  reduced. 
The  portions  of  the  canal  below  these  points  must  then  be  so 
fixed  as  to  preserve  the  same  rate  of  motion  in  the  water. 
This  is  done  by  decreasing  the  width  and  depth  of  the  canal, 
and  increasing  the  slope  of  the  bed.  Thus  starting  with  a 


DRAINAGE   CANALS.  471 

water-way  100  feet  wide,  6  feet  deep,  having  a  slope  of  6 
inches  to  the  mile,  the  width  of  water-way,  as  the  water  is 
drawn  off,  may  be  contracted  to  80,  60,  40,  and  20  feet  with 
the  corresponding  depths,  5-J-,  5,  4J,  and  4  feet ;  to  keep  the 
velocity  uniform  the  bed  should  have  slopes  of  6.4,  7,  7.9,  and 
10.3  inches  per  mile. 

655.  An  irrigation  canal  may  be  used  for  the  purposes  of 
navigation.  In  this  case  the  principles  already  laid  down 
for  navigable  canals  equally  apply,  with  the  condition,  how- 
ever, that  the  velocity  of  the  current  in  the  canal  should  not 
be  so  slight  as  to  injure  its  uses  as  an  irrigation  canal,  nor  so 
swift  as  to  offer  too  great  a  resistance  to  the  boats  using  it 
as  a  navigable  canal. 


DBAINAGE   CANALS. 

656.  Canals  of  this  class  are  the  reverse  of  irrigation  canals. 
They  are  used  to  carry  off  the  superfluous  water  which  falls 
on  or  flows  over  the  land. 

The  water-levels  of  canals  for  drainage,  to  be  effective, 
should  at  all  times  be  at  least  three  feet  below  the  level  of 
the  ground. 

Each  channel  for  the  water  should  have  an  area  and  decliv- 
ity, when  subjected  to  the  most  unfavorable  conditions,  suffi- 
cient to  discharge  all  the  water  that  it  receives  as  fast  as  this 
water  flows  in,  without  its  water-level  rising  so  high  as  to 
obstruct  the  flow  from  its  branches  or  to  flood  the  country. 

Hence,  to  plan  such  a  system  the  greatest  annual  rain-fall 
of  the  district,  and  the  greatest  fall  in  a  short  period  or  flood 
must  be  known. 

Where  the  land  to  be  drained  is  below  the  level  of  high 
water,  the  area  to  be  drained  must  be  protected  by  embank- 
ments. The  canals  are  then  laid  off  on  the  plan  just  given, 
and  the  water  from  the  main  canals  is  removed  by  pumping, 

Drainage  canals  may  be  divided  into  two  classes:  open 
and  covered.  Where  pure  water  is  to  be  removed,  the  former 
are  -used ;  when  filthy  water,  or  foul  materials,  are  to  be  re- 
moved, the  latter  are  used,  and  are  known  then  as  sewers. 
Sewerage  is  the  special  name  used  to  designate  the  drainage 
of  a  city  or  town,  in  which  the  foul  waters  and  refuse  are 
collected  and  discharged  by  sewers. 

As  far  as  the  principles  of  construction  are  concerned  sewers 
do  not  differ  from  the  works  already  described.  Especial  at- 
tention must  be  paid  to  prevent  the  escape  of  the*  foul  gaa 
*nd  disagreeable  odors  from  the  drains. 


4:72  CIVIL   ENGINEERING. 


CANALS   FOE    SUPPLYING   CITIES   AND   TOWNS   WITH    WATER. 

657.  As  sewers  are  only  particular  cases  of  drainage  canals, 
so  canals  for  supplying  cities  with  water  are  only  particular 
cases  of  irrigation  canals,  and  are  therefore  governed  by  the 
same  general  principles  in  their  construction. 

The  canals  of  this  class  are  usually  covered,  and  receive  the 
general  name  of  aqueducts. 

658.  The  health  and  comfort  of  the  residents  of  cities  and 
towns  are  so  dependent  upon  a  proper  supply  of  water  and  a 
good  system  of  sewerage  that  the  greatest  care  must  be  taken 
by  the  engineer  that  no  mistakes  are  made  by  him  in  planning 
and  constructing  either  of  these    systems.     The  principles 
which  regulate  in  deciding  upon  the  quantity  of  water  re- 
quired, the  means  and  purity  of  the  supply,  the  location  of  the 
reservoirs,  the  method  of  distribution,  etc.,  form  a  subject 
which  can  be  considered  in  a  special  treatise  only.     The  same 
remark  applies  also  to  sewerage. 


